You should not be asking for us to give a tutorial is logic. That is not what the forum is about.

If you have a specific question, then post it. We will try to help.

Having said that, here is some remarks on your first question.

is true if and only ifboth A & B are true.

So if we negate that statement, , then that means that at least one of the conjuncts is false.

That is .

The converse relies upon .