Boolean Logic Example
•Download as PPTX, PDF•
0 likes•904 views
This document discusses proving the Boolean logic problem B + A (B + C) + BC = B + AC. It first expands the brackets in the left side of the equation, then looks for common elements to combine like terms. After expanding and combining terms, it arrives at the right side of the equation, proving the identities are equal.
Report
Share
Report
Share
Recommended
In class work 26 feb
The document summarizes the proof of a conjecture from class. It shows that given A ∩ B ⊆ C and Ac ∩ B ⊆ C, it can be proven that B ⊆ C. The proof has two parts: first, it shows that (A ∩ B) ∩ (Ac ∩ B) ⊆ C. Second, it proves that (A ∩ B) ∩ (Ac ∩ B) = B. Bringing these steps together proves the original conjecture that B ⊆ C.
The five laws of boolean algebra
The Five Laws of Boolean Algebra outline fundamental properties of binary logic operations. The Commutative Law states that addition and multiplication are commutative. The Associative Law specifies that addition and multiplication are associative. The Distributive Law describes how multiplication distributes over addition. The Identity Law establishes that adding or multiplying any value with itself yields the original value. The Redundancy Law denotes that redundant operations can be simplified.
Camila´s presentation
The document contains questions and answers about various science topics including the three main states of matter (solid, liquid, gas), the definition of matter, how to remove energy from matter by lowering temperature or increasing volume, that lightning and stars contain plasma, the shape of liquids, where Bose-Einstein condensates can be found, that rainbows contain seven colors, examples of natural and artificial light, and concepts like reflection, refraction, and how prisms can split white light into colors.
21st inmo 06
1) In a triangle where the sides form an arithmetic progression, the incentre I is perpendicular to one of the sides BI extended. I is also the circumcentre of another triangle formed from the midpoints of sides of the original triangle.
2) For any positive integer n, there exists a unique pair of positive integers (a,b) such that a formula involving n, a and b is satisfied.
3) Find all integer triples (a,b,c) that remain unchanged when a function mapping triples to triples is applied twice.
4) In a 9x9 chessboard with 46 randomly colored squares, there must exist a 2x2 block of squares with at least 3 squares colored
Distributive property
The document discusses the distributive property in mathematics. It explains that the distributive property means taking something and sharing it around, such as multiplying a term outside parentheses by each term inside. It also discusses the FOIL method for distributing terms in multiplication, where the First, Outer, Inner, and Last terms of two expressions joined by multiplication are each multiplied individually. Finally, it notes the key insights that ab + a = a(b+1) and shows deMorgan's laws.
Boolean Logic
Boolean logic represents true and false values using 1s and 0s. It uses various operators like AND, OR, NOT to combine boolean variables. Truth tables define the output for every possible combination of input variables. Boolean expressions can be written in sum of products form or minterm form. Boolean logic is used in digital circuits, computer science, and mathematics.
Successful search strategies
The document discusses different strategies for searching the internet and databases, including where to search, how search engines work, and the differences between search engines, directories, and metasearchers. It recommends using keywords for specific searches and exploring the advanced features of search tools like Google.
Systematic search strategies
This document provides guidance on developing a systematic and comprehensive search strategy for systematic reviews. It explains that a systematic search strategy is essential to capture all relevant studies on a topic. The strategy should include synonyms for key concepts, Boolean operators to combine terms, and subject headings from different databases. It provides an example of developing a search strategy based on turning a research question into PICO components and combining population, intervention, comparison, and outcome terms. The search strategy example spans multiple slides and databases to model a comprehensive approach.
Recommended
In class work 26 feb
The document summarizes the proof of a conjecture from class. It shows that given A ∩ B ⊆ C and Ac ∩ B ⊆ C, it can be proven that B ⊆ C. The proof has two parts: first, it shows that (A ∩ B) ∩ (Ac ∩ B) ⊆ C. Second, it proves that (A ∩ B) ∩ (Ac ∩ B) = B. Bringing these steps together proves the original conjecture that B ⊆ C.
The five laws of boolean algebra
The Five Laws of Boolean Algebra outline fundamental properties of binary logic operations. The Commutative Law states that addition and multiplication are commutative. The Associative Law specifies that addition and multiplication are associative. The Distributive Law describes how multiplication distributes over addition. The Identity Law establishes that adding or multiplying any value with itself yields the original value. The Redundancy Law denotes that redundant operations can be simplified.
Camila´s presentation
The document contains questions and answers about various science topics including the three main states of matter (solid, liquid, gas), the definition of matter, how to remove energy from matter by lowering temperature or increasing volume, that lightning and stars contain plasma, the shape of liquids, where Bose-Einstein condensates can be found, that rainbows contain seven colors, examples of natural and artificial light, and concepts like reflection, refraction, and how prisms can split white light into colors.
21st inmo 06
1) In a triangle where the sides form an arithmetic progression, the incentre I is perpendicular to one of the sides BI extended. I is also the circumcentre of another triangle formed from the midpoints of sides of the original triangle.
2) For any positive integer n, there exists a unique pair of positive integers (a,b) such that a formula involving n, a and b is satisfied.
3) Find all integer triples (a,b,c) that remain unchanged when a function mapping triples to triples is applied twice.
4) In a 9x9 chessboard with 46 randomly colored squares, there must exist a 2x2 block of squares with at least 3 squares colored
Distributive property
The document discusses the distributive property in mathematics. It explains that the distributive property means taking something and sharing it around, such as multiplying a term outside parentheses by each term inside. It also discusses the FOIL method for distributing terms in multiplication, where the First, Outer, Inner, and Last terms of two expressions joined by multiplication are each multiplied individually. Finally, it notes the key insights that ab + a = a(b+1) and shows deMorgan's laws.
Boolean Logic
Boolean logic represents true and false values using 1s and 0s. It uses various operators like AND, OR, NOT to combine boolean variables. Truth tables define the output for every possible combination of input variables. Boolean expressions can be written in sum of products form or minterm form. Boolean logic is used in digital circuits, computer science, and mathematics.
Successful search strategies
The document discusses different strategies for searching the internet and databases, including where to search, how search engines work, and the differences between search engines, directories, and metasearchers. It recommends using keywords for specific searches and exploring the advanced features of search tools like Google.
Systematic search strategies
This document provides guidance on developing a systematic and comprehensive search strategy for systematic reviews. It explains that a systematic search strategy is essential to capture all relevant studies on a topic. The strategy should include synonyms for key concepts, Boolean operators to combine terms, and subject headings from different databases. It provides an example of developing a search strategy based on turning a research question into PICO components and combining population, intervention, comparison, and outcome terms. The search strategy example spans multiple slides and databases to model a comprehensive approach.
Elementary Internet Search Strategies: The Information Treasure Hunt
Tutorial video designed to teach beginning users effective search strategies for conducting online research. Targeted for elementary students in grades 2-5.
Search Strategies
The document discusses search strategies for reference librarians. It outlines the search process which includes verifying and categorizing the question, identifying appropriate resources and search types, translating the question for the resources, conducting the search, and delivering the information. The document emphasizes understanding how to find information even if you don't know everything by knowing the relationship between reference interviews and search strategies.
Boolean logic presentation
This document introduces Boolean logic and how it can be used to make decisions in computer programming. The lesson aims to explore using true/false logic to make decisions. An example is given of using "if/then" statements to decide whether to take an umbrella based on weather conditions. Boolean logic allows combining true/false conditions with AND, OR, and NOT to make complex decisions. The goal is to use these concepts to create instructions for a computer to choose what to bring outside based on the weather.
Boolean Logic
This document discusses Boolean logic and digital logic basics. It covers topics like logic gates (AND, OR, NOT), transistors, truth tables, precedence rules, NAND and NOR gates, integration levels from SSI to VLSI, logical expressions, equivalence, and Boolean algebra properties.
Online Search Techniques-Boolean Searching
Boolean searching is a technique that uses Boolean operators like AND, OR and NOT to conduct more precise online searches. It was named after mathematician George Boole who developed a system of logic for better search results. AND narrows results by requiring all search terms, OR expands them by including either term, and NOT limits by excluding specific terms. Boolean logic allows combining terms and nesting search statements for optimal results, though implementation varies across search systems.
Binary Operation Boolean Logic
The document discusses binary operations and Boolean logic. It defines binary operations like addition, subtraction, multiplication and division. It then explains Boolean logic operations like AND, OR and NOT. Truth tables are provided to define the output for all inputs of the NOT, AND and OR operations. Examples of Boolean logic expressions and their corresponding truth tables are also given.
Ch 5 boolean logic
Boolean logic is a form of mathematics that represents true and false values. It was outlined by George Boole in 1854 and forms the basis of modern computing. There are three basic Boolean logic operations - AND, OR, and NOT - that allow combining true and false values to form compound conditions. Logical comparisons and operators are used to evaluate conditions as either true or false, and these values can then be manipulated using Boolean logic.
Boolean Logic
1) George Boole first developed Boolean algebra in 1854 to represent logical operations using algebra, which became important for computer applications.
2) Boolean logic uses operators like AND, OR, and NOT to narrow or broaden the scope of searches.
3) Examples are provided of how Boolean operators function when combined in different ways in a search.
Boolean logic
George Boole was a mathematician and philosopher who invented Boolean logic, which is used in database searching to combine terms. Boolean logic uses operators like AND, OR, and NOT to refine search results by requiring multiple concepts, using synonyms, distinguishing meanings, or eliminating specific topics. Practicing Boolean logic helps understand how to use operators to increase recall of information or focus search results.
Boolean- Search Basics
This document discusses Boolean logic and search operators that can be used to refine searches. It explains the basic Boolean operators - AND, OR, and NOT - and how they combine search terms. Specifically, it provides examples of using OR to search for terms in combination, AND to find terms that co-occur, and NOT to exclude certain terms. The document also covers techniques like phrase searching using quotation marks, grouping terms with parentheses, and using modifiers like asterisks to expand searches. The goal is to illustrate how Boolean logic and operators can help users cast broad searches initially and then progressively narrow them down to the most relevant results.
Boolean Logic: how to talk to search engines in their own language
George Boole, a famous mathematician, invented Boolean logic which uses AND and OR operators to combine search terms. Boolean logic allows search engines to understand what information a user is looking for. AND produces results that include all search terms while OR produces results that include any of the search terms. Using Boolean operators such as AND and OR allows users to more precisely define their search queries to find relevant information.
Boolean+logic
George Boole published "An Investigation into the Laws of Thought" in 1854, outlining a system of logic and algebraic language dealing with true and false values. This became known as Boolean logic. Boolean logic uses only true and false values and the basic operations are AND, OR, and NOT. Boolean logic is the basis for modern computing, as electronic circuits can represent Boolean operations using gates. Circuits called AND, OR, and NOT gates perform the corresponding logical operations and form the building blocks for digital logic.
Boolean Logic Searching: A Primer
This document provides an overview of Boolean logic searching and how it applies to internet searches. It discusses the three Boolean operators - AND, OR, and NOT - and how they combine search terms using set logic and Venn diagrams. While few search engines support full Boolean searches with operators, most use implied Boolean logic where spaces mean AND and symbols like "+" and "-" stand in for operators. Many also provide search forms that allow choosing logic (e.g. "this" or "all" terms) without using operators. The document provides examples of constructing searches using the different methods.
Web of knowledge advanced features
This document provides instructions for using various features of the Web of Knowledge database, including registering an account, saving searches, creating search and citation alerts, and using the citation map tool. It notes that the interface is expected to be redesigned in January 2014 and free webinars are available to preview the changes.
Bad websites
This document summarizes and critiques 5 bad websites. The websites are criticized for having non-eye catching titles, inconsistent fonts, random stock images, bland or garish color schemes, irrelevant pictures, lots of GIFs, translations that don't translate the page, busy images that block text, and failure to clearly communicate what the company does or sells. In general, the websites break rules of good design and usability.
Debugging and Tuning Mobile Web Sites with Modern Web Browsers
Until recently, debugging a mobile web site was incredibly difficult. Luckily things things have changed. Now some desktop browsers not only contain remote debuggers, but have other features to monitor and improve performance and detect memory leaks.
How to search the Internet, a guide to save time and effort
A guide on how to conduct a search of the Internet, using a range of techniques to locate the information required. It might seem simple but this guide could save hours of research. Searching just got easier. From the Northampton Business Directory team.
Internet Search
This document provides tips and strategies for making internet searches more productive. It demonstrates how to effectively use keywords and search operators in Google to find specific types of information and filter results. Various Google tools are described that can help organize searches, including Google Scholar, Google News, Google Alerts, and options to customize search experiences for students or collaboratively with other teachers.
How to develop modern web application framework
The document discusses how to develop the plugin architecture of a modern web application framework (WAF). It describes what the plugin architecture of a WAF should be, including making the core elements small and extensible. It then covers developing plugin types that can hook into the WAF lifecycle or add methods to classes. As an example, it outlines how the Angelos WAF implements a plugin system using Mouse roles and method modifiers to hook into component hook points. It concludes by stressing that WAF developers should provide default plugin sets for common needs.
Windows 8 and the Cloud
This document provides an overview of using Windows 8 and Windows Azure cloud services together. It discusses how the cloud enables unlimited power, storage and collaboration. It introduces SkyDrive for cloud file storage and sharing. It describes using cloud media in Windows 8 apps and having server backends hosted in the cloud. It also covers using Windows Azure mobile services for syncing offline data to the cloud and accessing cloud APIs and data. The document recommends several additional cloud resources for learning more.
Karnaugh Mapping Explained
The document discusses using Karnaugh mapping to solve problems by mapping logic functions with variables onto a grid. It provides an example of a Karnaugh mapping problem involving variables A, B, and C to determine the function Z. Simplification rules and grouping adjacent cells are used to make variables redundant.
Op Amp Revision Q1
The document describes a voltage amplifier circuit that uses feedback. It asks to derive an expression for the closed-loop voltage gain Gv in terms of the open-loop gain Avo and feedback fraction β. The derivation shows that the closed-loop voltage gain Gv is equal to the open-loop gain Avo divided by the feedback fraction β.
More Related Content
Viewers also liked
Elementary Internet Search Strategies: The Information Treasure Hunt
Tutorial video designed to teach beginning users effective search strategies for conducting online research. Targeted for elementary students in grades 2-5.
Search Strategies
The document discusses search strategies for reference librarians. It outlines the search process which includes verifying and categorizing the question, identifying appropriate resources and search types, translating the question for the resources, conducting the search, and delivering the information. The document emphasizes understanding how to find information even if you don't know everything by knowing the relationship between reference interviews and search strategies.
Boolean logic presentation
This document introduces Boolean logic and how it can be used to make decisions in computer programming. The lesson aims to explore using true/false logic to make decisions. An example is given of using "if/then" statements to decide whether to take an umbrella based on weather conditions. Boolean logic allows combining true/false conditions with AND, OR, and NOT to make complex decisions. The goal is to use these concepts to create instructions for a computer to choose what to bring outside based on the weather.
Boolean Logic
This document discusses Boolean logic and digital logic basics. It covers topics like logic gates (AND, OR, NOT), transistors, truth tables, precedence rules, NAND and NOR gates, integration levels from SSI to VLSI, logical expressions, equivalence, and Boolean algebra properties.
Online Search Techniques-Boolean Searching
Boolean searching is a technique that uses Boolean operators like AND, OR and NOT to conduct more precise online searches. It was named after mathematician George Boole who developed a system of logic for better search results. AND narrows results by requiring all search terms, OR expands them by including either term, and NOT limits by excluding specific terms. Boolean logic allows combining terms and nesting search statements for optimal results, though implementation varies across search systems.
Binary Operation Boolean Logic
The document discusses binary operations and Boolean logic. It defines binary operations like addition, subtraction, multiplication and division. It then explains Boolean logic operations like AND, OR and NOT. Truth tables are provided to define the output for all inputs of the NOT, AND and OR operations. Examples of Boolean logic expressions and their corresponding truth tables are also given.
Ch 5 boolean logic
Boolean logic is a form of mathematics that represents true and false values. It was outlined by George Boole in 1854 and forms the basis of modern computing. There are three basic Boolean logic operations - AND, OR, and NOT - that allow combining true and false values to form compound conditions. Logical comparisons and operators are used to evaluate conditions as either true or false, and these values can then be manipulated using Boolean logic.
Boolean Logic
1) George Boole first developed Boolean algebra in 1854 to represent logical operations using algebra, which became important for computer applications.
2) Boolean logic uses operators like AND, OR, and NOT to narrow or broaden the scope of searches.
3) Examples are provided of how Boolean operators function when combined in different ways in a search.
Boolean logic
George Boole was a mathematician and philosopher who invented Boolean logic, which is used in database searching to combine terms. Boolean logic uses operators like AND, OR, and NOT to refine search results by requiring multiple concepts, using synonyms, distinguishing meanings, or eliminating specific topics. Practicing Boolean logic helps understand how to use operators to increase recall of information or focus search results.
Boolean- Search Basics
This document discusses Boolean logic and search operators that can be used to refine searches. It explains the basic Boolean operators - AND, OR, and NOT - and how they combine search terms. Specifically, it provides examples of using OR to search for terms in combination, AND to find terms that co-occur, and NOT to exclude certain terms. The document also covers techniques like phrase searching using quotation marks, grouping terms with parentheses, and using modifiers like asterisks to expand searches. The goal is to illustrate how Boolean logic and operators can help users cast broad searches initially and then progressively narrow them down to the most relevant results.
Boolean Logic: how to talk to search engines in their own language
George Boole, a famous mathematician, invented Boolean logic which uses AND and OR operators to combine search terms. Boolean logic allows search engines to understand what information a user is looking for. AND produces results that include all search terms while OR produces results that include any of the search terms. Using Boolean operators such as AND and OR allows users to more precisely define their search queries to find relevant information.
Boolean+logic
George Boole published "An Investigation into the Laws of Thought" in 1854, outlining a system of logic and algebraic language dealing with true and false values. This became known as Boolean logic. Boolean logic uses only true and false values and the basic operations are AND, OR, and NOT. Boolean logic is the basis for modern computing, as electronic circuits can represent Boolean operations using gates. Circuits called AND, OR, and NOT gates perform the corresponding logical operations and form the building blocks for digital logic.
Boolean Logic Searching: A Primer
This document provides an overview of Boolean logic searching and how it applies to internet searches. It discusses the three Boolean operators - AND, OR, and NOT - and how they combine search terms using set logic and Venn diagrams. While few search engines support full Boolean searches with operators, most use implied Boolean logic where spaces mean AND and symbols like "+" and "-" stand in for operators. Many also provide search forms that allow choosing logic (e.g. "this" or "all" terms) without using operators. The document provides examples of constructing searches using the different methods.
Web of knowledge advanced features
This document provides instructions for using various features of the Web of Knowledge database, including registering an account, saving searches, creating search and citation alerts, and using the citation map tool. It notes that the interface is expected to be redesigned in January 2014 and free webinars are available to preview the changes.
Bad websites
This document summarizes and critiques 5 bad websites. The websites are criticized for having non-eye catching titles, inconsistent fonts, random stock images, bland or garish color schemes, irrelevant pictures, lots of GIFs, translations that don't translate the page, busy images that block text, and failure to clearly communicate what the company does or sells. In general, the websites break rules of good design and usability.
Debugging and Tuning Mobile Web Sites with Modern Web Browsers
Until recently, debugging a mobile web site was incredibly difficult. Luckily things things have changed. Now some desktop browsers not only contain remote debuggers, but have other features to monitor and improve performance and detect memory leaks.
How to search the Internet, a guide to save time and effort
A guide on how to conduct a search of the Internet, using a range of techniques to locate the information required. It might seem simple but this guide could save hours of research. Searching just got easier. From the Northampton Business Directory team.
Internet Search
This document provides tips and strategies for making internet searches more productive. It demonstrates how to effectively use keywords and search operators in Google to find specific types of information and filter results. Various Google tools are described that can help organize searches, including Google Scholar, Google News, Google Alerts, and options to customize search experiences for students or collaboratively with other teachers.
How to develop modern web application framework
The document discusses how to develop the plugin architecture of a modern web application framework (WAF). It describes what the plugin architecture of a WAF should be, including making the core elements small and extensible. It then covers developing plugin types that can hook into the WAF lifecycle or add methods to classes. As an example, it outlines how the Angelos WAF implements a plugin system using Mouse roles and method modifiers to hook into component hook points. It concludes by stressing that WAF developers should provide default plugin sets for common needs.
Windows 8 and the Cloud
This document provides an overview of using Windows 8 and Windows Azure cloud services together. It discusses how the cloud enables unlimited power, storage and collaboration. It introduces SkyDrive for cloud file storage and sharing. It describes using cloud media in Windows 8 apps and having server backends hosted in the cloud. It also covers using Windows Azure mobile services for syncing offline data to the cloud and accessing cloud APIs and data. The document recommends several additional cloud resources for learning more.
Viewers also liked (20)
Elementary Internet Search Strategies: The Information Treasure Hunt
Elementary Internet Search Strategies: The Information Treasure Hunt
Boolean Logic: how to talk to search engines in their own language
Boolean Logic: how to talk to search engines in their own language
Debugging and Tuning Mobile Web Sites with Modern Web Browsers
Debugging and Tuning Mobile Web Sites with Modern Web Browsers
How to search the Internet, a guide to save time and effort
How to search the Internet, a guide to save time and effort
More from ml4ml4
Karnaugh Mapping Explained
The document discusses using Karnaugh mapping to solve problems by mapping logic functions with variables onto a grid. It provides an example of a Karnaugh mapping problem involving variables A, B, and C to determine the function Z. Simplification rules and grouping adjacent cells are used to make variables redundant.
Op Amp Revision Q1
The document describes a voltage amplifier circuit that uses feedback. It asks to derive an expression for the closed-loop voltage gain Gv in terms of the open-loop gain Avo and feedback fraction β. The derivation shows that the closed-loop voltage gain Gv is equal to the open-loop gain Avo divided by the feedback fraction β.
Op Amp Revision Q2
When designing non-critical voltage amplifier circuits using operational amplifiers, designers assume the amplifiers have ideal characteristics including infinite voltage gain, infinite input impedance, zero output impedance, and no frequency dependence. These ideal characteristics allow simplifying assumptions that negative feedback forces the voltage difference between the inverting and non-inverting terminals to zero and no current flows into any operational amplifier terminal.
Op Amp Revision Q4
The switching threshold voltages and hysteresis for an inverting comparator with VREF=+2.5V and resistors R1=10kΩ and R2=15kΩ are:
The high threshold voltage (VH) is 3.5V. The low threshold voltage (VL) is 0.5V. The hysteresis is 4V, calculated as the difference between the high and low threshold voltages.
Op Amp Revision Q3
The ideal operational amplifier configuration shown in Figure 3 has two input terminals at 0V. Applying network analysis, the output voltage is calculated to be -4V, assuming a current i1 flows from voltage V1 and a current i2 flows from V2. The op amp properties and Kirchhoff's laws are used to relate the input and output voltages and currents.
Synchronous Logic Circuit Revision Q
An example of Synchronous Logic Circuit showing state changes and clock pulses. 1st year electronics.
Formative Summative Presentation
This document discusses the differences between summative and formative assessment, and describes a new approach to formative assessment implemented with students. Summative assessment evaluates student learning at a point in time, while formative assessment is intended to promote continued improvement. The approach implemented weekly formative assessments using different technologies to provide students with prompt feedback, which research shows improves learning. Key factors for effective formative assessment include timely feedback, balancing strengths and weaknesses, focusing feedback, and making feedback useful for students.
High Quality Teaching Presentation
The presentation introduces developments to establish Platinum quality teaching within the Faculty of Advanced Engineering. It overviews initiatives already implemented, including personal tutoring groups and professional development sessions. Current collaborations starting include working with student representatives and international campuses. Future plans discussed establishing peer mentoring, meaningful module feedback, and training staff in virtual learning platforms.
Learning&Teaching Fellow Presentation
The Learning & teaching Fellow assisting University academics to embrace the new Virtual Learning Environment technology
More from ml4ml4 (9)
Boolean Logic Example
- 1. Boolean Logic Problems Prove that B + A (B + C) + BC = B + AC B + A (B + C) + BC First expand the brackets B + AB + AC + BC Now look for terms with common elements B(1 + A ) + AC + BC But 1 + A = 1 B + AC + BC = B + BC + AC Look for more terms with common elements B(1 + C) + AC = B + AC