Chapter SR28, Problem 12P

Solution

Tell whether the bi-conditional statement is true or false. Explain.

True.

Given:

An integer is odd if and only if it is not even.

Concept used:

• A bi-conditional statement is a statement that has the words “if and only if”. You can write a conditional statement and its converse together as a bi-conditional statement.
• A bi-conditional statement is true only when the conditional statement and its converse are both true.

Calculation:

Given - An integer is odd if and only if it is not even.

Conditional: If the integer is odd then it is not even. True.

Converse: If the integer is not even then it is odd. True.

The bi-conditional statement is true because the conditional and its converse both are true.