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Truth table  how would solve this problem? p ^ ~p = p v~p

Truth table  how would solve this problem? p ^ ~p = p v~p

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 7RE
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Truth table 

how would solve this problem?

p ^ ~p =

p v~p

 

Expert Solution
Step 1

Let us construct the truth table for the given statement 

p ^ ~p

~ is called negation operator, that is ~p is true if and only if p is false and vice versa.

∧is called logical conjunction, the statement p and ~p  is true only if both are true, otherwise it is false.

p   ~p p ^ ~p
T F F
F T F

If all the entries in the final column is false, then it is called as Contradiction.

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