* Identify, write, and analyze conditional statements
* Write the inverse, converse, and contrapositive of a conditional statement
* Write a counterexample to a false conjecture
* Write a biconditional statement
* Identify, write, and analyze the truth value of conditional statements.
* Write the inverse, converse, and contrapositive of a conditional statement.
This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
* Identify, write, and analyze the truth value of conditional statements.
* Write the inverse, converse, and contrapositive of a conditional statement.
This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
Polynomials are algebraic expressions that are consist of variables and coefficients. We can perform arithmetic operations such as subtraction, addition, multiplication and division. This presentation is all about factoring completely different types of polynomials. There four types of polynomials to factor that would be discuss in this presentation
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
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This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
Polynomials are algebraic expressions that are consist of variables and coefficients. We can perform arithmetic operations such as subtraction, addition, multiplication and division. This presentation is all about factoring completely different types of polynomials. There four types of polynomials to factor that would be discuss in this presentation
If you are looking for math video tutorials (with voice recording), you may download it on our YouTube Channel. Don't forget to SUBSCRIBE for you to get updated on our upcoming videos.
https://tinyurl.com/y9muob6q
Also, please do visit our page, LIKE and FOLLOW us on Facebook!
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
Identify, write, and analyze conditional statements.
Write the converse, inverse, and contrapositive of a conditional statement.
Write biconditional statements.
* Identify, write, and analyze conditional statements
* Write the inverse, converse, and contrapositive of a conditional statement
* Write a counterexample to a fake conjecture
The student is able to (I can):
Use inductive reasoning to identify patterns and make conjectures
Find counterexamples to disprove conjectures
Identify, write, and analyze the truth value of conditional statements.
Write the inverse, converse, and contrapositive of a conditional statement.
* Model exponential growth and decay
* Use Newton's Law of Cooling
* Use logistic-growth models
* Choose an appropriate model for data
* Express an exponential model in base e
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
* Find the distance between two points
* Find the midpoint of two given points
* Find the coordinates of an endpoint given one endpoint and a midpoint
* Find the coordinates of a point a fractional distance from one end of a segment
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Introduce functions and function notation
* Develop skills in constructing and interpreting the graphs of functions
* Learn to apply this knowledge in a variety of situations
* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
* Identify intervals on which a function increases, decreases, or is constant
* Use graphs to locate relative maxima or minima
* Test for symmetry
* Identify even or odd functions and recognize their symmetries
* Understand and use piecewise functions
* Solve polynomial equations by factoring
* Solve equations with radicals and check the solutions
* Solve equations with rational exponents
* Solve equations that are quadratic in form
* Solve absolute value equations
* Determine whether a relation or an equation represents a function.
* Evaluate a function.
* Use the vertical line test to identify functions.
* Identify the domain and range of a function from its graph
* Identify intercepts from a function’s graph
* Solve counting problems using the Addition Principle.
* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
* Find the common ratio for a geometric sequence.
* List the terms of a geometric sequence.
* Use a recursive formula for a geometric sequence.
* Use an explicit formula for a geometric sequence.
* Find the common difference for an arithmetic sequence.
* Write terms of an arithmetic sequence.
* Use a recursive formula for an arithmetic sequence.
* Use an explicit formula for an arithmetic sequence.
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
This slides describes the basic concepts of ICT, basics of Email, Emerging Technology and Digital Initiatives in Education. This presentations aligns with the UGC Paper I syllabus.
Exploiting Artificial Intelligence for Empowering Researchers and Faculty, In...Dr. Vinod Kumar Kanvaria
Exploiting Artificial Intelligence for Empowering Researchers and Faculty,
International FDP on Fundamentals of Research in Social Sciences
at Integral University, Lucknow, 06.06.2024
By Dr. Vinod Kumar Kanvaria
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Model Attribute Check Company Auto PropertyCeline George
In Odoo, the multi-company feature allows you to manage multiple companies within a single Odoo database instance. Each company can have its own configurations while still sharing common resources such as products, customers, and suppliers.
A review of the growth of the Israel Genealogy Research Association Database Collection for the last 12 months. Our collection is now passed the 3 million mark and still growing. See which archives have contributed the most. See the different types of records we have, and which years have had records added. You can also see what we have for the future.
This slide is special for master students (MIBS & MIFB) in UUM. Also useful for readers who are interested in the topic of contemporary Islamic banking.
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
A workshop hosted by the South African Journal of Science aimed at postgraduate students and early career researchers with little or no experience in writing and publishing journal articles.
South African Journal of Science: Writing with integrity workshop (2024)
1.3.1 Conditional Statements
1. Conditional Statements
The student is able to (I can):
• Identify, write, and analyze conditional statements.
• Write the inverse, converse, and contrapositive of a
conditional statement.
• Write a counterexample to a false conjecture.
2. conditionalconditionalconditionalconditional statementstatementstatementstatement – a statement that can be written as
an “if-then” statement.
Example: IfIfIfIf today is Saturday, thenthenthenthen we don’t have to go to
school.
hypothesishypothesishypothesishypothesis – the part of the conditional followingfollowingfollowingfollowing the word
“if” (underline once).
“today is Saturday” is the hypothesis.
conclusionconclusionconclusionconclusion – the part of the conditional followingfollowingfollowingfollowing the word
“then” (underline twice).
“we don’t have to go to school” is the conclusion.
3. Examples
NotationNotationNotationNotation
Conditional statement: p → q, where
p is the hypothesis and
q is the conclusion.
Identify the hypothesis and conclusion:
1. If I want to buy a book, then I need
some money.
2. If today is Thursday, then tomorrow is
Friday.
3. Call your parents if you are running late.
4. Examples
NotationNotationNotationNotation
Conditional statement: p → q, where
p is the hypothesis and
q is the conclusion.
Identify the hypothesis and conclusion:
1. If I want to buy a book, then I need
some money.
2. If today is Thursday, then tomorrow is
Friday.
3. Call your parents if you are running late.
5. Examples
To write a statement as a conditional,
identify the sentence’s hypothesis and
conclusion by figuring out which part of the
statement depends on the other.
Write a conditional statement:
• Two angles that are complementary are
acute.
• Even numbers are divisible by 2.
6. Examples
To write a statement as a conditional,
identify the sentence’s hypothesis and
conclusion by figuring out which part of the
statement depends on the other.
Write a conditional statement:
• Two angles that are complementary are
acute.
If two angles are complementary, then
they are acute.
• Even numbers are divisible by 2.
If a number is even, then it is divisible
by 2.
7. To prove a conjecture false, you just have to come up with a
counterexample.
• The hypothesis must be the samesamesamesame as the conjecture’s and
the conclusion is differentdifferentdifferentdifferent.
Example: Write a counterexample to the statement, “If a
quadrilateral has four right angles, then it is a square.”
8. To prove a conjecture false, you just have to come up with a
counterexample.
• The hypothesis must be the samesamesamesame as the conjecture’s and
the conclusion is differentdifferentdifferentdifferent.
Example: Write a counterexample to the statement, “If a
quadrilateral has four right angles, then it is a square.”
A counterexample would be a quadrilateral that has four
right angles (true hypothesis) but is not a square (different
conclusion). So a rectanglerectanglerectanglerectangle would work.
9. Examples Each of the conjectures is false. What
would be a counterexample?
If I get presents, then today is my birthday.
If Lamar is playing football tonight, then
today is Friday.
10. Examples Each of the conjectures is false. What
would be a counterexample?
If I get presents, then today is my birthday.
• A counterexample would be a day that I
get presents (true hyp.) that isn’t my
birthday (different conc.), such as
Christmas.
If Lamar is playing football tonight, then
today is Friday.
• Lamar plays football (true hyp.) on days
other than Friday (diff. conc.), such as
games on Thursday.
11. Examples Determine if each conditional is true. If
false, give a counterexample.
1. If your zip code is 76012, then you live
in Texas.
TrueTrueTrueTrue
2. If a month has 28 days, then it is
February.
September also has 28 days, which
proves the conditional false.
Texas
76012
12. negation ofnegation ofnegation ofnegation of pppp – “Not p”
Notation: ~p
Example: The negation of the statement “Blue is my favorite
color,” is “Blue is notnotnotnot my favorite color.”
Related ConditionalsRelated ConditionalsRelated ConditionalsRelated Conditionals SymbolsSymbolsSymbolsSymbols
Conditional p → q
Converse q → p
Inverse ~p → ~q
Contrapositive ~q →~p
13. Example: Write the conditional, converse, inverse, and
contrapositive of the statement:
“A cat is an animal with four paws.”
TypeTypeTypeType StatementStatementStatementStatement
Conditional
(p → q)
If an animal is a cat, then it has four
paws.
Converse
(q → p)
If an animal has four paws, then it is a
cat.
Inverse
(~p → ~q)
If an animal is not a cat, then it does not
have four paws.
Contrapositive
(~q → ~p)
If an animal does not have four paws,
then it is not a cat.
14. Example: Write the conditional, converse, inverse, and
contrapositive of the statement:
“When n2 = 144, n = 12.”
TypeTypeTypeType StatementStatementStatementStatement Truth ValueTruth ValueTruth ValueTruth Value
Conditional
(p → q)
If n2 = 144, then n = 12.
F
(n = –12)
Converse
(q → p)
If n = 12, then n2 = 144. T
Inverse
(~p → ~q)
If n2 ≠ 144, then n ≠ 12 T
Contrapositive
(~q → ~p)
If n ≠ 12, then n2 ≠ 144
F
(n = –12)
15. biconditionalbiconditionalbiconditionalbiconditional – a statement whose conditional and converse
are both true. It is written as
“pppp if and only ifif and only ifif and only ifif and only if qqqq”, “pppp iffiffiffiff qqqq”, or “pppp ↔↔↔↔ qqqq”.
To write the conditional statement and converse within the
biconditional, first identify the hypothesis and conclusion,
then write p → q and q → p.
A solution is a base iff it has a pH greater than 7.
p → q: If a solution is a base, then it has a pH greater than 7.
q → p: If a solution has a pH greater than 7, then it is a base.
16. Writing a biconditional statement:
1. Identify the hypothesis and conclusion.
2. Write the hypothesis, “if and only if”, and the conclusion.
Example: Write the converse and biconditional from:
If 4x + 3 = 11, then x = 2.
Converse: If x = 2, then 4x + 3 = 11.
Biconditional: 4x + 3 = 11 iff x = 2.