Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
xpand then reduce the proposition. Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p Select a law from below to apply to: ¬(w∨(p∧¬w))

xpand then reduce the proposition. Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p Select a law from below to apply to: ¬(w∨(p∧¬w))

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter2: Equations, Inequalities, And Problem Solving
Section2.6: More On Inequalities And Problem Solving
Problem 68PS
See similar textbooks
icon
Related questions
Question

Expand then reduce the proposition.

Simplify ¬(w∨(p∧¬w)) to ¬w∧¬p

Select a law from below to apply to: ¬(w∨(p∧¬w))
### 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. \(a \lor \neg a \equiv \text{T}\) 2. \(a \land \neg a \equiv \text{F}\) #### Negation Laws 1. \(\neg \text{T} \equiv \text{F}\) 2. \(\neg \text{F} \equiv \text{T}\) #### Identity Laws 1. \(a \lor \text{F} \equiv a\) 2. \(a \land \text{T} \equiv a\) #### Double Negation Law 1. \(\neg \neg a \equiv a\) This table summarizes fundamental logical equivalences used in Boolean algebra and set theory. These laws are essential for simplifying logical expressions and proving equivalences in logic and mathematics.
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. \(a \lor \neg a \equiv \text{T}\) 2. \(a \land \neg a \equiv \text{F}\) #### Negation Laws 1. \(\neg \text{T} \equiv \text{F}\) 2. \(\neg \text{F} \equiv \text{T}\) #### Identity Laws 1. \(a \lor \text{F} \equiv a\) 2. \(a \land \text{T} \equiv a\) #### Double Negation Law 1. \(\neg \neg a \equiv a\) This table summarizes fundamental logical equivalences used in Boolean algebra and set theory. These laws are essential for simplifying logical expressions and proving equivalences in logic and mathematics.
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
Algebra for College Students
Algebra for College Students
Algebra
ISBN:
9781285195780
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Intermediate Algebra
Intermediate Algebra
Algebra
ISBN:
9781285195728
Author:
Jerome E. Kaufmann, Karen L. Schwitters
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Holt Mcdougal Larson Pre-algebra: Student Edition…
Holt Mcdougal Larson Pre-algebra: Student Edition…
Algebra
ISBN:
9780547587776
Author:
HOLT MCDOUGAL
Publisher:
HOLT MCDOUGAL
SEE MORE TEXTBOOKS