Boolean algebra: How does the imply operator work?

Question

I am conflicted because our professor said that "(not) A implies B only and only if A and B = 0" which doesn't match with what I found on Wikipedia or other books on Boolean algebra: "A implies B = (not) A or B". Are the two equivalent, or one of them is wrong? Our professor also said that the imply operator is similar to a negated AND...

Answer 1

(not A) => B if only false when A is true and B is false. So if A and B are both true (not A) => B is true. But A and B = 0 is false. So these are not equivalent.

not (A => B) is only true when (A => B) is false. (A => B) is only false when A is true and B is false. So if A and B are both false, A and B = 0 is true but not(A => B) is false.

You must be misquoting your professor.

A or B = 0 is only true if A and B are both false. (not) A => B is only true if A and B are both false.

So that must be what your professor meant.