[–] 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.