   # Construct a truth table for each statement to determine if the statements are equivalent p → q , ∼ q → ∼ p ### Mathematical Excursions (MindTap C...

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

#### Solutions

Chapter
Section ### Mathematical Excursions (MindTap C...

4th Edition
Richard N. Aufmann + 3 others
Publisher: Cengage Learning
ISBN: 9781305965584
Chapter 3.3, Problem 58ES
Textbook Problem
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## Construct a truth table for each statement to determine if the statements are equivalent p → q , ∼ q → ∼ p

To determine

To construct a truth table to determine if the given statements are equivalent.

### Explanation of Solution

Given information:

Given statements are pq, ~q ~p

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

Now the statement pq is calculated. The statement contains 'implication', so the statement will be false only if a true statement implies a false statement. Else the statement will always be true.

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