Supply the reason for each step to show the equivalence of (pV ~ q) ^ (~ pV ~ q) and ~ q. ~(p V ~q) V (~p ^ ~q) = (~p ^q) V (~p^~q) Step 1. = ~pA (q V ~q) Step 2. =pAt Step 3. = mp Step 4. Therefore, (p V ~q) V (~p A ~q) = ~p.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 19E
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Write if Step 1,2,3,4 are either: Identity laws, De Morgan's law, Distributive laws, or Negation laws

Supply the reason for each step to show the equivalence of
(pV ~ q) ^ (~ pv ~ q) and ~ q.
(p V ~q) V (~p A ~q) = (~p ^q) V (~p ^ ~q) Step 1.
= ~p A (q V ~q)
Step 2.
= ~pAt
Step 3.
= ~p
Step 4.
Therefore, (p V ~q) V (~p ^ ~q) = ~p.
Transcribed Image Text:Supply the reason for each step to show the equivalence of (pV ~ q) ^ (~ pv ~ q) and ~ q. (p V ~q) V (~p A ~q) = (~p ^q) V (~p ^ ~q) Step 1. = ~p A (q V ~q) Step 2. = ~pAt Step 3. = ~p Step 4. Therefore, (p V ~q) V (~p ^ ~q) = ~p.
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