# Which biconditional is NOT a good definition?

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## Question:

Which biconditional is NOT a good definition?

A) An angle is straight if and only if its measure is 180.
B) A whole number is even if and only if it is divisible by 2.
C) A whole number is odd if and only if the number is not divisible by 2.
D) A ray is a bisector of an angle if and only if it splits the angle into two angles

A biconditional statement is a statement of the form:

P if and only if Q.

Where P and Q are two propositions, and this means that P is only true if Q is true, and Q is only true if P is true.

We will see that the correct option is D ” A ray is a bisector of an angle if and only if it splits the angle into two angles”

To see which one is the correct option, we need to see where we have a definition problem.

A) “An angle is straight if and only if its measure is 180.”

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A straight angle is a 180° angle, so this is correct.

B) ” A whole number is even if and only if it is divisible by 2.”

All even numbers are multiplies of 2, thus, all even numbers are divisible by 2, so this is correct.

C) “A whole number is odd if and only if the number is not divisible by 2.”

Odd numbers are all of these that are not multiples of 2. So all odd numbers are not divisible by 2, so this is correct.

D) “A ray is a bisector of an angle if and only if it splits the angle into two angles”

This is incorrect, the bisector splits the angle into two equal angles.

Then the biconditional that is not a good definition is the last one, option D.