If a number is a multiple of 4, it is divisible by 2.

Which of these is a logically equivalent statement?

If a number is divisible by 2, it is a multiple of 4.

If a number is not divisible by 2, it is a multiple of 4.

If a number is not a multiple of 4, it is not divisible by 2.

If a number is not divisible by 2, it is not a multiple of 4.

I am pretty sure it is the third one, but will someone check my work?

Question

If a number is a multiple of 4, it is divisible by 2.
 
Which of these is a logically equivalent statement?



If a number is divisible by 2, it is a multiple of 4.

If a number is not divisible by 2, it is a multiple of 4.

If a number is not a multiple of 4, it is not divisible by 2.

If a number is not divisible by 2, it is not a multiple of 4.

I am pretty sure it is the third one,  but will someone check my work?

oaktree · Answer

The last. If the statement is true, then its contra-positive is also always true.

anonymous · Answer

Okay thank you.