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[–] antiracist ago 

What is the negation of (~A <-> B)

A iff B is only true when they're the same.

~A iff B is only true when A and B are different.

What is the opposite of them being different? That's what the question is asking. The answer is them being the same.

I put: (A <-> ~B)

This is the same as ~A iff B. Only true when they're different. The question didn't ask for a different way of saying the same thing. The question asked for the opposite.

If A=1 and B=0 then the truth value of ~(~A <-> ~B) is:

I put false.

The true answer is true. Your false answer is false.

The inside of the parentheses is "the same". That parentheses is only true when A and B are "the same".

When A=1 and B=0, they are not "the same". So that parentheses is false.

But there is a negation outside of the parentheses, so you flip the answer, and the final answer is true.