Q in description

Question

Which biconditional is not a good definition?



1. A whole number is odd if and only if the number is not divisible by 2.
2. An angle is straight if and only if its measure is 180°.
3. A whole number is even if and only if it is divisible by 2.
4. A ray is a bisector of an angle if and only if it splits the angle into two angles.

Answer 1

last option is not a biconditional

an angle is a bisector only if it splits the angle in two

but the converse is not true

if p then q

but not q then p

the bisector does split the angle in two

but only in a precise way, cutting the angle in 2 equal angles

Just splitting in angle into two separate angles doesn't guarantee they're be equal angles half the size of the original angle

the second option isn't fully correct either

true an angle is straight if its angle = 180 degrees

but not only if, as the angle could be 180n degrees where n = any integer

such as 0, +/-180, +/-360, +/-540, ...

Answer 2

1. A ray is a bisector of an angle if and only if it splits the angle into two angles.