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This document discusses inductive and deductive reasoning. It provides examples of each type of reasoning and how they differ. Inductive reasoning involves examining specific examples to reach a general conclusion, while deductive reasoning starts with a general statement and uses logical principles to reach a specific conclusion. The document also provides examples of logic puzzles and how deductive reasoning can be used to solve them by organizing the clues and data provided.

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Reasoning

The document discusses different types of reasoning including inductive reasoning and deductive reasoning. It provides examples of each type of reasoning and how they are used. Inductive reasoning involves making generalizations based on specific examples, while deductive reasoning uses general statements to logically prove a specific conclusion. The document explains how to use Venn diagrams to determine if a deductive argument is valid or invalid.

Problem Solving and Reasoning

Problem solving is the process of finding solutions to difficult or complex issues ,w hile reasoning is the action of thinking about something in a logical, sensible way.

Probability of Simple and Compound Events

This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.

probabilityofsimpleandcompoundevents-190217133041.pptx

Here are the solutions to the probability questions:
1. The probability of picking a Geometry book first is 3/8. The probability of picking an Algebra book second is 5/7. By the multiplication principle, the probability of picking a Geometry book first and an Algebra book second is (3/8) × (5/7) = 15/56.
2. The probability of picking a vowel (E, O, A) from Bag 1 is 3/5. The probability of picking a consonant (V, L, D, R, Z) from Bag 2 is 5/7. By the multiplication principle, the probability of picking a vowel from Bag 1 and a consonant from Bag 2 is (

DLL-M8- November 4-8,2019.docx

This document summarizes a math teacher's daily lesson log for a week of teaching 8th grade students. Each day covers objectives, content, learning resources and procedures. Objectives include understanding logic/reasoning and communicating arguments. Content covered inductive/deductive reasoning through examples like number patterns. Learning resources included textbooks and materials. Procedures involved reviewing, presenting new concepts, examples, discussions and assessments. The log concludes with remarks on student performance, challenges encountered, and innovations discovered.

1.1 patterns & inductive reasoning

The document discusses the importance of finding patterns and using inductive reasoning in geometry and mathematics. It provides examples of describing patterns, making conjectures based on examples, and using inductive reasoning to form hypotheses about general cases. Students are instructed on how to look for patterns, make conjectures, and verify or find counterexamples for conjectures.

ตัวจริง

Inductive and deductive reasoning are two important types of logical reasoning.
[1] Inductive reasoning involves observing specific examples and patterns to derive a general conclusion. [2] Deductive reasoning uses logical rules and known statements to derive a conclusion. [3] Venn diagrams can help determine the validity of deductive arguments by visually representing logical relationships between categories.

3 PROBABILITY TOPICSFigure 3.1 Meteor showers are rare, .docx

This document provides an introduction to probability topics including terminology, rules, and examples. It defines key terms like sample space, event, probability, mutually exclusive events, independent events, and conditional probability. Examples are given to demonstrate calculating probabilities of events from sample spaces using the addition and multiplication rules. The document also discusses representing sample spaces and events using Venn diagrams, contingency tables, and tree diagrams.

Reasoning

The document discusses different types of reasoning including inductive reasoning and deductive reasoning. It provides examples of each type of reasoning and how they are used. Inductive reasoning involves making generalizations based on specific examples, while deductive reasoning uses general statements to logically prove a specific conclusion. The document explains how to use Venn diagrams to determine if a deductive argument is valid or invalid.

Problem Solving and Reasoning

Problem solving is the process of finding solutions to difficult or complex issues ,w hile reasoning is the action of thinking about something in a logical, sensible way.

Probability of Simple and Compound Events

This document contains a lesson plan on probability for students. It begins with definitions of key probability terms and examples of calculating probabilities of simple and compound events. It then provides word problems for students to practice calculating probabilities. The document concludes with additional practice problems for students to answer. The overall document provides instruction and practice on fundamental concepts in probability.

probabilityofsimpleandcompoundevents-190217133041.pptx

Here are the solutions to the probability questions:
1. The probability of picking a Geometry book first is 3/8. The probability of picking an Algebra book second is 5/7. By the multiplication principle, the probability of picking a Geometry book first and an Algebra book second is (3/8) × (5/7) = 15/56.
2. The probability of picking a vowel (E, O, A) from Bag 1 is 3/5. The probability of picking a consonant (V, L, D, R, Z) from Bag 2 is 5/7. By the multiplication principle, the probability of picking a vowel from Bag 1 and a consonant from Bag 2 is (

DLL-M8- November 4-8,2019.docx

This document summarizes a math teacher's daily lesson log for a week of teaching 8th grade students. Each day covers objectives, content, learning resources and procedures. Objectives include understanding logic/reasoning and communicating arguments. Content covered inductive/deductive reasoning through examples like number patterns. Learning resources included textbooks and materials. Procedures involved reviewing, presenting new concepts, examples, discussions and assessments. The log concludes with remarks on student performance, challenges encountered, and innovations discovered.

1.1 patterns & inductive reasoning

The document discusses the importance of finding patterns and using inductive reasoning in geometry and mathematics. It provides examples of describing patterns, making conjectures based on examples, and using inductive reasoning to form hypotheses about general cases. Students are instructed on how to look for patterns, make conjectures, and verify or find counterexamples for conjectures.

ตัวจริง

Inductive and deductive reasoning are two important types of logical reasoning.
[1] Inductive reasoning involves observing specific examples and patterns to derive a general conclusion. [2] Deductive reasoning uses logical rules and known statements to derive a conclusion. [3] Venn diagrams can help determine the validity of deductive arguments by visually representing logical relationships between categories.

3 PROBABILITY TOPICSFigure 3.1 Meteor showers are rare, .docx

This document provides an introduction to probability topics including terminology, rules, and examples. It defines key terms like sample space, event, probability, mutually exclusive events, independent events, and conditional probability. Examples are given to demonstrate calculating probabilities of events from sample spaces using the addition and multiplication rules. The document also discusses representing sample spaces and events using Venn diagrams, contingency tables, and tree diagrams.

G8 MATHEMATICS REASONING MATHEMATICS.docx

The document outlines a mathematics lesson plan on deductive and inductive reasoning for 8th grade students. The lesson plan includes objectives, content, learning resources, procedures, activities and evaluation. Students will learn the differences between deductive and inductive reasoning, perform examples of each, and assess their understanding through group activities and practice questions. The goal is for students to understand and apply both types of reasoning in mathematics and everyday life.

Beauty and Applicability of Mathematics.pptx

This document discusses various topics in mathematics including infinity, counting infinite sets, and Georg Cantor's work on establishing the existence of uncountable sets. Some key points:
- Georg Cantor proved that the set of real numbers is uncountable by showing that there is no one-to-one correspondence between the real numbers in the interval [0,1) and the natural numbers.
- Cantor introduced the notion of cardinal numbers to quantify the "size" of infinite sets. He denoted the cardinality of the natural numbers as א0.
- Cantor hypothesized that there is no set with a cardinality between that of the natural numbers (א0) and the real numbers (2

Inductive and Deductive Reasoning.pptx

This lesson aims to introduce to you the world of reasoning and logic. Reasoning is one vital skill in studying Mathematics and its vast landscape for learning. Even in real world setting, one can use reasoning to prove or
disprove concepts or information. As learner of this lesson, you are expected
to achieve the minimum competency for this topic which is to use inductive
or deductive reasoning in an argument.

Probability - The Basics Workshop 1

The first of two workshops I've created for children in my class about probability. This is used as a rotation activity after I have done some teaching on it first.

Deductive and Inductive Reasoning with Vizzini

This document provides information on deductive and inductive reasoning. It defines key logic and reasoning terms such as premise, conclusion, argument, and syllogism. It explains deductive reasoning as deriving logical conclusions from general statements and premises. An example is provided of the classic "All men are mortal, Socrates is a man, therefore Socrates is mortal" syllogism. Inductive reasoning is explained as deriving probable conclusions from specific observations, rather than guaranteed conclusions. Examples of both deductive and inductive reasoning are given from geometry, sequences, and the movie The Princess Bride to illustrate the differences between the two types of reasoning.

Ideas for teaching chance, data and interpretation of data

These activities have been designed specifically for Year 3 students according to the Australian Curriculum guidelines. However, they can be adapted to meet other standards or year levels.

Recreational mathematics magazine number 2 september_2014

This document summarizes several hat puzzles:
1. An old hat puzzle is presented where logicians in a line each guess the color of their own hat based on seeing the colors of hats in front of them. A strategy is discussed to maximize the number who guess correctly.
2. A new variation is introduced where logicians can have hats of any color from a finite set of colors. The same strategy works to ensure all but the last logician guesses their hat color correctly.
3. The reader is presented with a new hat puzzle to solve.

The University of Maine at Augusta Name ______.docx

The University of Maine at Augusta Name: ________________________
Mathematics Department Date: _________________________
MAT 280 F16 Location:______________________
MAT 280
Exam 1 Chapter 1.1-1.6
Please answer the following questions. Part credit is possible if the work indicates an understanding of
the objective under investigation. Students may use their laptops, tablets, textbooks, notes, calculators
and scrap paper. If used, scrap paper should be turned in with the exam. Students may not use smart
phones. If available homework should be turned in with the exam.
Time: 2:45 If staff is available, extra time is permitted.
1. Find a proposition with the given truth table.
p q ?
T T F
T F T
F T T
F F T
2. Write the truth table for the proposition (r q) (p → r). Use as many columns as necessary.
Label each column.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
3. Find a proposition using only pq and the connective V with the given truth table.
p
q
?
T T F
T F F
F T F
F F T
4. Determine whether p (q r) is equivalent to q (p r). Use as many columns as necessary.
Label each used column. Credit will only be when a completed truth table accompanies the answer.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
5. Write a proposition equivalent to ( p q) using only pq and the connective . . Support your
answer with a truth table. If necessary, insert columns in the truth table below to support your
answer
p
q
T T
T F
F T
F F
6. Prove that q p and its contrapositive are logically equivalent. If they are not equivalent, explain
why. Do the same for its inverse.
p
q
p
q
T T T T
T F T F
F T F T
F F F F
7. In the questions below write the statement in the form “If …, then ….”
a. Whenever the temperature drops below 35 degrees, children should wear boots
during recess.
b. You have completed your program’s requirements only if you are eligible to graduate.
Name: ________________________
8. Write the contrapositive, converse, and inverse of the following:
If I have a valid passport, I will be able to travel to Cuba.
.
a. Contrapositive:
b. Converse:
c. Inverse:
9. How many rows are required to show the truth table for the following compound proposition?
(q r ) → (p s) ...

scientific investigation hypothesis and problem.pptx

The document outlines the six steps of the scientific method which are identifying a problem, formulating a hypothesis, collecting data, testing the hypothesis through experimentation, analyzing the data, and making a conclusion. It provides examples of each step and has interactive elements where the user must correctly identify each step in a series of questions and activities related to experimentation and the scientific process. The goal is to help the user learn and understand the logical progression of the scientific method used by scientists.

(7) Lesson 9.2

The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
There are 6 combinations that result in a sum of 10 out of the total possible combinations when rolling two number cubes, which is 6^2 = 36 possible outcomes.
Therefore, the theoretical probability is 5/36.

Random variable

The document is a prayer asking God for guidance and blessings in one's studies and work. It asks God to pour forth brilliance on the intellect to dissipate darkness of sin and ignorance. It asks for a penetrating mind to understand, a retentive memory, ease in learning, lucidity to comprehend, and grace in expressing oneself. It asks God to guide the beginning, direct the progress, and bring the work to completion, through Jesus Christ.

Course Design Best Practices

1. Think “Relevant ==> Simple ==> Intricate.”
2. Visualize “mastery blocks.”
3. Generate comprehensive examples.
4. Assessment.
5. End with lead to next topic.

DLL_WEEK3_LC39-40.docx

This document contains a daily lesson plan for a mathematics class. It outlines the objectives, content, learning resources, procedures, and assessment for a lesson on the union and intersection of events and probability of simple events. The procedures include activities like games and word problems to illustrate and practice these concepts. Formative assessment is conducted through worksheets requiring students to calculate probabilities and analyze Venn diagrams showing relationships between events. The lesson aims to help students understand and apply probability concepts in real-world decision making.

LAILA BALINADO COT 2.pptx

Here are the answers to the probability questions about rolling a standard 6-sided die written on a single sheet of paper:
The faces of a cube are labelled 1, 2, 3, 4, 5, and 6. The cube is rolled once.
- What is the probability that the number on the top of the cube will be odd?
Favourable outcomes: 1, 3, 5
Probability = 3/6 = 1/2
- What is the probability that the number on the top of the cube will be greater than 5?
Favourable outcomes: 6
Probability = 1/6
- What is the probability that the number on the top of the cube will be a multiple

(7) Lesson 9.7

To determine the probability of two independent events occurring:
1. Find the probability of each individual event. For example, if spinning a spinner with four equal sections and rolling a six-sided die, the probability of each event would be 1/4 and 1/6 respectively.
2. Multiply the probabilities of the individual events. Since independent events do not influence each other, we can treat them as separate occurrences.
3. The product of the individual probabilities is the probability the two independent events will both occur. Continuing the spinner and die example, the probability of a specific outcome on the spinner AND a specific outcome on the die is (1/4) × (1/6) = 1/

inductive-and-deductive-reasoning-ppt.pptx

This document contrasts deductive and inductive reasoning.
Deductive reasoning involves drawing a specific conclusion from general premises, as in a syllogism with a valid argument structure. Inductive reasoning involves drawing a general conclusion based on observations or patterns in specific cases, where the conclusion is not guaranteed. Venn diagrams can illustrate the validity of deductive arguments by showing set relationships.

Probability distribution of a random variable module

This document provides an overview of a module on statistics and probability for senior high school students. It covers basic concepts of random variables and probability distributions through two lessons. The first lesson defines random variables and distinguishes between discrete and continuous variables. The second lesson defines discrete probability distributions and shows how to construct a histogram for a probability mass function. Examples are provided to illustrate key concepts. Learning competencies focus on understanding and applying random variables and probability distributions to real-world problems.

COT4 Lesson Plan Grade 8

This document summarizes a daily lesson plan for a Grade 8 mathematics class on probability. The lesson plan covers key concepts of probability including calculating the probability of simple events and appreciating its importance in daily life. Example probability problems are provided to help students understand concepts like determining possible outcomes and calculating probabilities. A quiz is used to evaluate student learning, and additional activities are suggested for students requiring remediation.

Skimbleshanks-The-Railway-Cat by T S Eliot

Skimbleshanks-The-Railway-Cat by T S Eliot

NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...

NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS

G8 MATHEMATICS REASONING MATHEMATICS.docx

The document outlines a mathematics lesson plan on deductive and inductive reasoning for 8th grade students. The lesson plan includes objectives, content, learning resources, procedures, activities and evaluation. Students will learn the differences between deductive and inductive reasoning, perform examples of each, and assess their understanding through group activities and practice questions. The goal is for students to understand and apply both types of reasoning in mathematics and everyday life.

Beauty and Applicability of Mathematics.pptx

This document discusses various topics in mathematics including infinity, counting infinite sets, and Georg Cantor's work on establishing the existence of uncountable sets. Some key points:
- Georg Cantor proved that the set of real numbers is uncountable by showing that there is no one-to-one correspondence between the real numbers in the interval [0,1) and the natural numbers.
- Cantor introduced the notion of cardinal numbers to quantify the "size" of infinite sets. He denoted the cardinality of the natural numbers as א0.
- Cantor hypothesized that there is no set with a cardinality between that of the natural numbers (א0) and the real numbers (2

Inductive and Deductive Reasoning.pptx

This lesson aims to introduce to you the world of reasoning and logic. Reasoning is one vital skill in studying Mathematics and its vast landscape for learning. Even in real world setting, one can use reasoning to prove or
disprove concepts or information. As learner of this lesson, you are expected
to achieve the minimum competency for this topic which is to use inductive
or deductive reasoning in an argument.

Probability - The Basics Workshop 1

The first of two workshops I've created for children in my class about probability. This is used as a rotation activity after I have done some teaching on it first.

Deductive and Inductive Reasoning with Vizzini

This document provides information on deductive and inductive reasoning. It defines key logic and reasoning terms such as premise, conclusion, argument, and syllogism. It explains deductive reasoning as deriving logical conclusions from general statements and premises. An example is provided of the classic "All men are mortal, Socrates is a man, therefore Socrates is mortal" syllogism. Inductive reasoning is explained as deriving probable conclusions from specific observations, rather than guaranteed conclusions. Examples of both deductive and inductive reasoning are given from geometry, sequences, and the movie The Princess Bride to illustrate the differences between the two types of reasoning.

Ideas for teaching chance, data and interpretation of data

These activities have been designed specifically for Year 3 students according to the Australian Curriculum guidelines. However, they can be adapted to meet other standards or year levels.

Recreational mathematics magazine number 2 september_2014

This document summarizes several hat puzzles:
1. An old hat puzzle is presented where logicians in a line each guess the color of their own hat based on seeing the colors of hats in front of them. A strategy is discussed to maximize the number who guess correctly.
2. A new variation is introduced where logicians can have hats of any color from a finite set of colors. The same strategy works to ensure all but the last logician guesses their hat color correctly.
3. The reader is presented with a new hat puzzle to solve.

The University of Maine at Augusta Name ______.docx

The University of Maine at Augusta Name: ________________________
Mathematics Department Date: _________________________
MAT 280 F16 Location:______________________
MAT 280
Exam 1 Chapter 1.1-1.6
Please answer the following questions. Part credit is possible if the work indicates an understanding of
the objective under investigation. Students may use their laptops, tablets, textbooks, notes, calculators
and scrap paper. If used, scrap paper should be turned in with the exam. Students may not use smart
phones. If available homework should be turned in with the exam.
Time: 2:45 If staff is available, extra time is permitted.
1. Find a proposition with the given truth table.
p q ?
T T F
T F T
F T T
F F T
2. Write the truth table for the proposition (r q) (p → r). Use as many columns as necessary.
Label each column.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
3. Find a proposition using only pq and the connective V with the given truth table.
p
q
?
T T F
T F F
F T F
F F T
4. Determine whether p (q r) is equivalent to q (p r). Use as many columns as necessary.
Label each used column. Credit will only be when a completed truth table accompanies the answer.
p Ans: p q r
T T T
T T F
T F T
T F F
F T T
F T F
F F T
F F F
Name: ________________________
5. Write a proposition equivalent to ( p q) using only pq and the connective . . Support your
answer with a truth table. If necessary, insert columns in the truth table below to support your
answer
p
q
T T
T F
F T
F F
6. Prove that q p and its contrapositive are logically equivalent. If they are not equivalent, explain
why. Do the same for its inverse.
p
q
p
q
T T T T
T F T F
F T F T
F F F F
7. In the questions below write the statement in the form “If …, then ….”
a. Whenever the temperature drops below 35 degrees, children should wear boots
during recess.
b. You have completed your program’s requirements only if you are eligible to graduate.
Name: ________________________
8. Write the contrapositive, converse, and inverse of the following:
If I have a valid passport, I will be able to travel to Cuba.
.
a. Contrapositive:
b. Converse:
c. Inverse:
9. How many rows are required to show the truth table for the following compound proposition?
(q r ) → (p s) ...

scientific investigation hypothesis and problem.pptx

The document outlines the six steps of the scientific method which are identifying a problem, formulating a hypothesis, collecting data, testing the hypothesis through experimentation, analyzing the data, and making a conclusion. It provides examples of each step and has interactive elements where the user must correctly identify each step in a series of questions and activities related to experimentation and the scientific process. The goal is to help the user learn and understand the logical progression of the scientific method used by scientists.

(7) Lesson 9.2

The theoretical probability of rolling a sum of 10 when rolling two number cubes is 5/36.
There are 6 possible ways to roll a sum of 10: (1,9), (2,8), (3,7), (4,6), (5,5), (6,4).
There are 6 combinations that result in a sum of 10 out of the total possible combinations when rolling two number cubes, which is 6^2 = 36 possible outcomes.
Therefore, the theoretical probability is 5/36.

Random variable

The document is a prayer asking God for guidance and blessings in one's studies and work. It asks God to pour forth brilliance on the intellect to dissipate darkness of sin and ignorance. It asks for a penetrating mind to understand, a retentive memory, ease in learning, lucidity to comprehend, and grace in expressing oneself. It asks God to guide the beginning, direct the progress, and bring the work to completion, through Jesus Christ.

Course Design Best Practices

1. Think “Relevant ==> Simple ==> Intricate.”
2. Visualize “mastery blocks.”
3. Generate comprehensive examples.
4. Assessment.
5. End with lead to next topic.

DLL_WEEK3_LC39-40.docx

This document contains a daily lesson plan for a mathematics class. It outlines the objectives, content, learning resources, procedures, and assessment for a lesson on the union and intersection of events and probability of simple events. The procedures include activities like games and word problems to illustrate and practice these concepts. Formative assessment is conducted through worksheets requiring students to calculate probabilities and analyze Venn diagrams showing relationships between events. The lesson aims to help students understand and apply probability concepts in real-world decision making.

LAILA BALINADO COT 2.pptx

Here are the answers to the probability questions about rolling a standard 6-sided die written on a single sheet of paper:
The faces of a cube are labelled 1, 2, 3, 4, 5, and 6. The cube is rolled once.
- What is the probability that the number on the top of the cube will be odd?
Favourable outcomes: 1, 3, 5
Probability = 3/6 = 1/2
- What is the probability that the number on the top of the cube will be greater than 5?
Favourable outcomes: 6
Probability = 1/6
- What is the probability that the number on the top of the cube will be a multiple

(7) Lesson 9.7

To determine the probability of two independent events occurring:
1. Find the probability of each individual event. For example, if spinning a spinner with four equal sections and rolling a six-sided die, the probability of each event would be 1/4 and 1/6 respectively.
2. Multiply the probabilities of the individual events. Since independent events do not influence each other, we can treat them as separate occurrences.
3. The product of the individual probabilities is the probability the two independent events will both occur. Continuing the spinner and die example, the probability of a specific outcome on the spinner AND a specific outcome on the die is (1/4) × (1/6) = 1/

inductive-and-deductive-reasoning-ppt.pptx

This document contrasts deductive and inductive reasoning.
Deductive reasoning involves drawing a specific conclusion from general premises, as in a syllogism with a valid argument structure. Inductive reasoning involves drawing a general conclusion based on observations or patterns in specific cases, where the conclusion is not guaranteed. Venn diagrams can illustrate the validity of deductive arguments by showing set relationships.

Probability distribution of a random variable module

This document provides an overview of a module on statistics and probability for senior high school students. It covers basic concepts of random variables and probability distributions through two lessons. The first lesson defines random variables and distinguishes between discrete and continuous variables. The second lesson defines discrete probability distributions and shows how to construct a histogram for a probability mass function. Examples are provided to illustrate key concepts. Learning competencies focus on understanding and applying random variables and probability distributions to real-world problems.

COT4 Lesson Plan Grade 8

This document summarizes a daily lesson plan for a Grade 8 mathematics class on probability. The lesson plan covers key concepts of probability including calculating the probability of simple events and appreciating its importance in daily life. Example probability problems are provided to help students understand concepts like determining possible outcomes and calculating probabilities. A quiz is used to evaluate student learning, and additional activities are suggested for students requiring remediation.

G8 MATHEMATICS REASONING MATHEMATICS.docx

G8 MATHEMATICS REASONING MATHEMATICS.docx

Beauty and Applicability of Mathematics.pptx

Beauty and Applicability of Mathematics.pptx

Inductive and Deductive Reasoning.pptx

Inductive and Deductive Reasoning.pptx

Probability Grade 10 Third Quarter Lessons

Probability Grade 10 Third Quarter Lessons

Basic Concepts of Probability_updated_Tm_31_5_2.ppt

Basic Concepts of Probability_updated_Tm_31_5_2.ppt

Probability - The Basics Workshop 1

Probability - The Basics Workshop 1

Deductive and Inductive Reasoning with Vizzini

Deductive and Inductive Reasoning with Vizzini

Ideas for teaching chance, data and interpretation of data

Ideas for teaching chance, data and interpretation of data

Recreational mathematics magazine number 2 september_2014

Recreational mathematics magazine number 2 september_2014

The University of Maine at Augusta Name ______.docx

The University of Maine at Augusta Name ______.docx

scientific investigation hypothesis and problem.pptx

scientific investigation hypothesis and problem.pptx

(7) Lesson 9.2

(7) Lesson 9.2

Random variable

Random variable

Course Design Best Practices

Course Design Best Practices

DLL_WEEK3_LC39-40.docx

DLL_WEEK3_LC39-40.docx

LAILA BALINADO COT 2.pptx

LAILA BALINADO COT 2.pptx

(7) Lesson 9.7

(7) Lesson 9.7

inductive-and-deductive-reasoning-ppt.pptx

inductive-and-deductive-reasoning-ppt.pptx

Probability distribution of a random variable module

Probability distribution of a random variable module

COT4 Lesson Plan Grade 8

COT4 Lesson Plan Grade 8

Skimbleshanks-The-Railway-Cat by T S Eliot

Skimbleshanks-The-Railway-Cat by T S Eliot

NIPER 2024 MEMORY BASED QUESTIONS.ANSWERS TO NIPER 2024 QUESTIONS.NIPER JEE 2...

NIPER JEE PYQ
NIPER JEE QUESTIONS
MOST FREQUENTLY ASK QUESTIONS
NIPER MEMORY BASED QUWSTIONS

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Bonku-Babus-Friend by Sathyajith Ray for class 9 ksb

A Visual Guide to 1 Samuel | A Tale of Two Hearts

These slides walk through the story of 1 Samuel. Samuel is the last judge of Israel. The people reject God and want a king. Saul is anointed as the first king, but he is not a good king. David, the shepherd boy is anointed and Saul is envious of him. David shows honor while Saul continues to self destruct.

How to Setup Default Value for a Field in Odoo 17

In Odoo, we can set a default value for a field during the creation of a record for a model. We have many methods in odoo for setting a default value to the field.

BÀI TẬP BỔ TRỢ TIẾNG ANH LỚP 8 - CẢ NĂM - FRIENDS PLUS - NĂM HỌC 2023-2024 (B...

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https://app.box.com/s/nrwz52lilmrw6m5kqeqn83q6vbdp8yzpCh-4 Forest Society and colonialism 2.pdf

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- 2. Learning Outcomes: At the end of this lesson, the students will be able to: 1. Analyze problems using different types of reasoning. 2. Apply different types of reasoning to justify statements and arguments made about mathematics and mathematical concepts.
- 4. INDUCTIVE REASONING It is the process of reaching a general conclusion by examining specific examples.
- 5. INDUCTIVE REASONING The conclusion formed by using inductive reasoning is often called a conjecture, since it may or may not be correct.
- 6. Example 1: Use inductive reasoning to predict the next number in each item. 1. 2,8,14,20,26, _____ 2. 1,2,5,10,17,26, _____
- 7. Example 2: A. Every sports car I have ever seen is red. Thus, all sports cars are red. B. The coin I pulled from the bag is a 5-peso coin. Another 5-peso coin is drawn from the bag. A third coin from the bag is again a 5-peso coin. Therefore, all the coins in the bag are 5-peso coins.
- 8. Example 3: Consider the following. Pick a number. Multiply the number by 4, add 8 to the product, divide the sum by 2, and subtract 5. Complete the above procedure for several different numbers. Use inductive reasoning to make a conjecture about the relationship between the size of the resulting number and the size of the original number.
- 9. Solution: Suppose we start with seven as the original number. Then repeat the process for different numbers. The procedure yields the following: We conjecture that the given procedure produces a number that is one less than twice the original number.
- 10. Remarks: When we use inductive reasoning, we have no guarantee that our conclusion is correct. Just because a pattern is true for a few cases, it does not mean the pattern will continue. A statement is a true statement provided that it is valid in all cases. If we can find one case for which a statement is not valid, called a counterexample, then it is a false statement.
- 11. DEDUCTIVE REASONING It is the process of reaching a conclusion by applying general assumptions, procedures, or principles.
- 12. DEDUCTIVE REASONING Deduction starts out with a general statement, or hypothesis, and examines the possibilities to reach a specific, logical conclusion.
- 13. Example 1: 1. All men are mortal. Kahwi is a man. Therefore, Kahwi is mortal. 2. Corresponding parts of congruent triangles are congruent. Triangle ABC is congruent to triangle DEF. Angle B and angle E are corresponding angles. Thus, angle B is congruent to angle E.
- 15. Determine if each of the following statement uses inductive or deductive reasoning. 1. Teacher Erica is an enthusiastic and passionate teacher. Therefore, all teachers are enthusiastic and passionate. 2. All dogs are animals. Dhai is a dog. Thus, Dhai is an animal. 3. I got low score on the first long exam. I just recently took the second long exam and I got low score. Therefore, I will also get a low score on the third long exam. IR DR IR
- 16. Determine if each of the following statement uses inductive or deductive reasoning. 4. My classmates are disrespectful toward our instructor. Hence, all students are disrespectful. 5. Last Wednesday it was raining. Today is Wednesday and it is raining. Therefore, on the next Wednesday, it will also rain. 6. For any right triangle, the Pythagorean Theorem holds. ABC is a right triangle, therefore for ABC the Pythagorean Theorem holds. 7. All basketball players in your school are tall, so all basketball players must be tall. IR IR DR IR
- 17. A logic puzzle is a puzzle deriving from the mathematics field of deduction. Logic puzzles can be solved by using deductive reasoning and by organizing the data in a given situation.
- 18. A logic puzzle is basically a description of an event or any situation. Using the clues provided, one has to piece together what actually happened. This involves clear and logical thinking, hence the term “logic” puzzles.
- 19. Example 1 Three musicians appeared at a concert. Their last names were Benton, Lanier, and Rosario. Each plays only one of the following instruments: guitar, piano, or saxophone. 1. Benton and the guitar player arrived at the concert together. 2. The saxophone player performed before Benton. 3. Rosario wished the guitar player good luck. Who played each instrument? Guitar Piano Saxophone Benton Lanier Rosario
- 20. Example 2 You have a basket containing ten apples. You have 10 friends, who each desire an apple. You give each of your friends, one apple. Now all your friends have one apple each, yet there is an apple remaining in the basket. How? Solution: ✎You give an apple to your first nine friends, and a basket with an apple to your tenth friend. Each friend has an apple, and one of them has it in a basket. ✎ Alternative answer: one friend already had an apple and put it in the basket.
- 21. Example 3 A census-taker knocks on a door, and asks the woman inside how many children she has and how old they are. “I have three daughters, their ages are whole numbers, and the product of their ages is 36,” says the mother. “That’s not enough information”, responds the census-taker. “I’d tell you the sum of their ages, but you’d still be stumped.” “I wish you’d tell me something more.” “Okay, my oldest daughter Annie likes dogs.” What are the ages of the three daughters (Zeitz, 2007)?
- 22. Solution: After the first reading, it seems impossible- there isn’t enough information to determine the ages. The product of the ages is 36, so there are only a few possible triples of ages. Here is a table of all the possibilities Age 1, 1,36 1, 2,18 1, 3, 12 1, 4, 9 1, 6, 6 2, 2, 9 2, 3, 6 3, 3, 4 Sum 38 21 16 14 13 13 11 10 Now we see what is going on. The mother’s second statement (“I’d tell you the sum of their ages, but you’d still be stumped.) gives valuable information. It tells that the ages are either 1,6,6 or 2,2,9, for in all other cases, knowledge of the sum would tell unambiguously what the ages are. The final clue now makes sense, it tells that there is an oldest daughter, eliminating 1, 6,6. The daughters are thus 2, 2, and 9 years old.

- Reasoning is a process based on experience and principles that allow one to arrive at a conclusion.
- Reasoning is a process based on experience and principles that allow one to arrive at a conclusion.
- We make generalizations from the part to the whole. If we are not careful, it can lead to erroneous or mistake conclusions:
- Conjecture- estimation or guess
- Each successive number is 6 larger than the preceding number.
- It is not enough that the deduction is logically sound; the assumption (1) must also be true. Consider the following: "1) All cats are red. 2) Kitty is a cat, therefore Kitty is red." It is logically valid but leads to a non-valid conclusion because not 'all cats are red'.
- In mathematics, deductive reasoning makes use of definitions, axioms, theorems and rules and inference.