Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Reduce the proposition using laws, including de Morgan's and conditional. Simplify (q∨n)∧¬(¬q∧n) to q Select a law from below to apply to: (q∨n)∧¬(¬q∧n

Reduce the proposition using laws, including de Morgan's and conditional. Simplify (q∨n)∧¬(¬q∧n) to q Select a law from below to apply to: (q∨n)∧¬(¬q∧n

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

Reduce the proposition using laws, including de Morgan's and conditional.

Simplify (q∨n)∧¬(¬q∧n) to q

Select a law from below to apply to: (q∨n)∧¬(¬q∧n)
 
 
### Laws of Logic #### Distributive Laws 1. \( (a \land b) \lor (a \land c) \equiv a \land (b \lor c) \) 2. \( (a \lor b) \land (a \lor c) \equiv a \lor (b \land c) \) #### Commutative Laws 1. \( a \lor b \equiv b \lor a \) 2. \( a \land b \equiv b \land a \) #### De Morgan's Laws 1. \( \neg (a \lor b) \equiv \neg a \land \neg b \) 2. \( \neg (a \land b) \equiv \neg a \lor \neg b \) #### Conditional Laws 1. \( a \rightarrow b \equiv \neg a \lor b \) 2. \( a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a) \) #### Complement Laws 1. \( a \lor \neg a \equiv T \) 2. \( a \land \neg a \equiv F \) 3. \( \neg T \equiv F \) 4. \( \neg F \equiv T \) #### Identity Laws 1. \( a \lor F \equiv a \) 2. \( a \land T \equiv a \) #### Double Negation Law 1. \( \neg \neg a \equiv a \) ### Explanation of Components - **Logical operators include**: - \( \lor \): Logical OR - \( \land \): Logical AND - \( \neg \): Logical NOT - \( \rightarrow \): Logical implication (if...then) - \( \leftrightarrow \): Logical biconditional (if and only if) - **Constants**: - \( T \): True - \( F \): False These laws govern the simplification and transformation of logical expressions in mathematical logic and computer science. Understanding these laws can assist in proving equivalences and solving logical problems more efficiently.
Transcribed Image Text:### Laws of Logic #### Distributive Laws 1. \( (a \land b) \lor (a \land c) \equiv a \land (b \lor c) \) 2. \( (a \lor b) \land (a \lor c) \equiv a \lor (b \land c) \) #### Commutative Laws 1. \( a \lor b \equiv b \lor a \) 2. \( a \land b \equiv b \land a \) #### De Morgan's Laws 1. \( \neg (a \lor b) \equiv \neg a \land \neg b \) 2. \( \neg (a \land b) \equiv \neg a \lor \neg b \) #### Conditional Laws 1. \( a \rightarrow b \equiv \neg a \lor b \) 2. \( a \leftrightarrow b \equiv (a \rightarrow b) \land (b \rightarrow a) \) #### Complement Laws 1. \( a \lor \neg a \equiv T \) 2. \( a \land \neg a \equiv F \) 3. \( \neg T \equiv F \) 4. \( \neg F \equiv T \) #### Identity Laws 1. \( a \lor F \equiv a \) 2. \( a \land T \equiv a \) #### Double Negation Law 1. \( \neg \neg a \equiv a \) ### Explanation of Components - **Logical operators include**: - \( \lor \): Logical OR - \( \land \): Logical AND - \( \neg \): Logical NOT - \( \rightarrow \): Logical implication (if...then) - \( \leftrightarrow \): Logical biconditional (if and only if) - **Constants**: - \( T \): True - \( F \): False These laws govern the simplification and transformation of logical expressions in mathematical logic and computer science. Understanding these laws can assist in proving equivalences and solving logical problems more efficiently.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS