Chapter SR28, Problem 11P

Solution

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

False.

Given:

The graph of a function is a parabola if and only if the function is $y=x^2$ .

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 - The graph of a function is a parabola if and only if the function is $y=x^2$ .

Conditional: If the function is $y=x^2$ then the graph of a function is a parabola. True.

Converse: If the graph of a function is a parabola then the function is $y=x^2$ . False.

The bi-conditional statement is false because the converse is not true.