Look at the statement below. If a number is a multiple of 4, it is divisible by 2. Which of these is a logically equivalent statement?

Question

Look at the statement below.     If a number is a multiple of 4, it is divisible by 2.     Which of these is a logically equivalent statement?

anonymous · Answer

Do you have some statements?

anonymous · Answer

yes sir, one second.

anonymous · Answer

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

anonymous · Answer

Well, let's go through them one by one. Have you covered propositional logic in your class?

anonymous · Answer

I believe so, yes.

anonymous · Answer

Excuse me, are you still there?

anonymous · Answer

Ok, let's call the proposition A that a number is divisible by 4, and the proposition B that a number is divisible by 2.
The statement in the question says:
$$A \implies B$$
Yes I am.

anonymous · Answer

Okay, can I tell you what i think it is ?

anonymous · Answer

"If a number is not divisible by 2, it is a multiple of 4." Means:
$$¬(B)\implies A$$
This doesn't make any sense as then we could negate this argument to get:
$$B \implies ¬(A)$$
Are you comfortable with my use of the negation symbol by the way?

anonymous · Answer

Yes go ahead, I'll tell you if you're right.

anonymous · Answer

If a number is divisible by 2, it is a multiple of 4., the same one as you chose, sir. So , i guess i was right ? (: . Thank you .

anonymous · Answer

No that's not right, 6 is divisible by 2 but it's not a multiple of 4.
In fact, the easiest way to do this might just be to see if you can think of counterexamples to the statements.

anonymous · Answer

What about this one, does it make sense?
" If a number is not a multiple of 4, it is not divisible by 2."
Can you think of a counterexample which disproves this?

directrix · Answer

If a number is a multiple of 4, it is divisible by 2. 
P: x is a multiple of 4
Q: x is divisible by 2
P=>Q
The logically equivalent statement of P=>Q is its contrapositive,
~Q => ~P.

If x is not divisible by 2, then x is not a multiple of 4.
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*If a number is not divisible by 2, it is not a multiple of 4.*
@ErickSoReal