3) A is false. B may be true or false. This is neither evidence for nor against the statement. These irrelevant cases have no bearing on someone's confidence on the truthfulness of the statement.
It's an interesting point to see conditionals in a way of verification or falsification. The classical logical principle follows then the rule that if it can't be falsified it's true. Whereas intuition from your view (as I understand it) says that only what can be verified (or falsified) can be true. This is a very demanding view of truth which combines truth with the possibility of determining it.
It could be seen as problematic to mix up the logical conditional with natural language intuitions of "if-then" but since it's about formalization of natural language it's a valid point to question those formalizations. (The same applies maybe to the concept of truth.)
If you take the empty set that contains no elements: The fact that it contains no elements can be used with the logical principle discussed here:
E.g. You get to the conclusion that the empty set is a subset (or identical) of every other set.
This is because subset is defined in the following way:
Be x,y sets:
x is a subset (or identical) of y iff For all z (z € x then z € y). ('€' means "is element of")
Since z € empty set is always false, the whole universal sentence is (for x = the empty set) always true no matter which set y is.
Insofar I have a problem in calling such things irrelevant.
That leads to the question what is the consequence of the intuition that there is a "not sure"-value. Do we introduce this third value and how does our logic then look like? Does it have consequences for mathematics (in a very wide sense) as well or only for natural language?