# Use a truth table to determine whether the given statement is a self-contradiction. p ∧ ( ∼ p ∧ q )

### Mathematical Excursions (MindTap C...

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

Chapter
Section

### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3.2, Problem 51ES
Textbook Problem
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## Use a truth table to determine whether the given statement is a self-contradiction. p ∧ ( ∼ p ∧ q )

To determine

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

### Explanation of Solution

Given information:

Given statement is p(~pq)

Calculation:

The standard truth table for two statements is given by,

 p q T T T F F T F F

Then the negations are calculated,

 p q ~p T T F T F F F T T F F T

Now the statement (~pq) is calculated. The statements contain 'and', so the statement will be true when both the statements are true. Else the statement will always be false.

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