A number is divisible by 6 if and only if it is divisible by 3?
If this is a T-F question, the answer is false. It is true that
if a number is divisible by 6, it also divisible by 3. This is true
because 6 is divisible by 3. However, the converse -- If a number
is divisible by 3, it is divisible by 6, is false. A counterexample
is 15. 15 is divisible by 3, but not by 6.
It becomes clearer if you split the question into its two
parts.
A number is divisible by 6 if it is divisible by 3? False. It
must also be divisible by 2.
A number is divisible by 6 only if it is divisible by 3?
True.