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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584

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Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3.2, Problem 50ES
Textbook Problem
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Use a truth table to determine whether the given statement is a self-contradiction.

( p p )

To determine

To determine whether the given statement is a self-contradiction.

Explanation of Solution

Given information:

Given statement is ~(p ~p)

Calculation:

The standard truth table for one statements is given by,

  p
T
F

Then the negations are calculated,

  p  ~p
TF
FT

Now the statement p ~p is calculated. The statements contain 'or', so the statement will be false when both the statements are false. Else the statement will always be true.

  p  ~p  p 

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