Question

consider the conditional statement, if the radius of a circle is 5, then the diameter is 10. what is the conditional statement written as a biconditional?
○ the radius of a circle is 5 if and only if the diameter is 10.
○ the radius of a circle is 10 if and only if the diameter is 5.
○ the radius of a circle is 15 if and only if the diameter is 5.
○ the radius of a circle is 5 if and only if the diameter is 5.

Explanation:

A biconditional statement combines a conditional statement and its converse, using "if and only if". The original conditional is "If radius is 5, then diameter is 10". The converse would be "If diameter is 10, then radius is 5" (since diameter = 2×radius, so radius = diameter/2; if diameter is 10, radius is 5). Combining these gives "The radius of a circle is 5 if and only if the diameter is 10". The other options have incorrect radius - diameter relationships (e.g., diameter should be twice the radius, not equal or with wrong numbers).

Answer:

A. The radius of a circle is 5 if and only if the diameter is 10.