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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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.
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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