Question

Which of the following is a biconditional statement?

A) If x2 = 25, then x = 5 or x = –5

B) x = 5 if x2 = 25

C) x = 5 if and only if x + 5 = 10

D) If x ≠ 5 then x2 ≠ 25

Answer 1

C) x = 5 if and only if x + 5 = 10

Explanation:

You want to identify the biconditional statement among those that are given.

Conditional

A conditional statement is of the form ...

If P, then Q.

Converse

The converse of the above conditional statement is ...

If Q, then P.

Biconditional

When both the statement and its converse are intended, the statement can be written as the biconditional ...

If and only if P then Q.

The given example of a biconditional statement is ...

x = 5 if and only if x +5 = 10.

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Additional comment

This can be abbreviated ...

Iff P then Q

meaning "if P then Q, and if Q then P", or "if and only if P, then Q."