Supply the reason for each step to show the equivalence of: (p∨∼q)∧(∼p∨∼q) and ∼q. note: Refer to the image and identify if it is De Morgan's Laws, Distributive Law, Negation law or Identity Law
Supply the reason for each step to show the equivalence of: (p∨∼q)∧(∼p∨∼q) and ∼q. note: Refer to the image and identify if it is De Morgan's Laws, Distributive Law, Negation law or Identity Law
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 25E
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Question
Supply the reason for each step to show the equivalence of:
(p∨∼q)∧(∼p∨∼q) and ∼q.
note: Refer to the image and identify if it is De Morgan's Laws, Distributive Law, Negation law or Identity Law.
![~(p V ~q) V (~p ^~q) = (~p ^q) V (~p^ ~q) Step 1.
= ~p ^ (q V ~q)
Step 2.
= ~p At
Step 3.
= ~p
Step 4.
Therefore, ~(p V ~q) V (~p ^ ~q) = ~p.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb54d7fb7-8bfa-4890-b88f-a4b79f8be9b8%2F18bc3eec-ef83-46f2-af1a-330e008d82a0%2F28np9hi_processed.jpeg&w=3840&q=75)
Transcribed Image Text:~(p V ~q) V (~p ^~q) = (~p ^q) V (~p^ ~q) Step 1.
= ~p ^ (q V ~q)
Step 2.
= ~p At
Step 3.
= ~p
Step 4.
Therefore, ~(p V ~q) V (~p ^ ~q) = ~p.
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