- If A is true, then B is false. 3. If A were true, then B would be false.
If you reflect a bit on them you should find out that these two examples work very differently. If the premise is not true in (2), then according to classical logic the whole conditional is vacuously true, the inference scheme remains valid but its particular application in (2) is not sound. The interesting case occurs when A is true (or at least you think so), which then allows you to conclude that B is false if you accept the argument in the first place.
But this cannot be how (3) works, because the subjunctive conditional already presupposes (or conventionally or pragmatically implicates, in other theories) that A is actually false. If that would suffice to make the whole subjunctive conditional true, all subjunctive conditionals would be true by virtue of their own presupposition (viz., their conventional or pragmatic implicature). This can't be quite right. If they make sense at all, we'd like some subjunctive conditionals to be true, and others to be false given that their premises are actually false, and, of course, this should be so for a reason. The idea is that we sort of imagine what the world would be like if A were true, and then check on the basis of this 'knowledge' whether B or not B would hold in that world. And that is where the mess starts, for there is no universal agreement of how to spell this out in formal terms and there are many competing explanations for the meaning of conditionals like (3). These types of sentences and their mood are also expressed very differently in different languages, there is interplay with the tenses and a lot of cross-linguistic variation.
To give you an idea of how different a semantics for (3) might be in comparison to an ordinary conditional, here is an example inspired by Lewis's conditional logic, though probably not identical to it. Order all possible worlds (=models of the logic) by some reflexive and transitive relation of closeness centred around the actual world. If w0 is the actual world, and w1, w2, w3 are other worlds, and e.g. w0 < w1 ~ w2 < w3, this means that w1 and w2 are equally close to the actual world and closer to it than w3. The counterfactual (3) then roughly means:
In all worlds in which A is true that are closest to the actual world (in which A is false), B is false.
If that is the case, the counterfactual is true, otherwise it is false.
People tried to spell out this closeness in terms of minimal change, e.g. by counting the number of changes to the assignments of truth and falsity to propositional variables you need to get from the actual world (viz. "the right model", current state of the universe) to the respective other world (viz. model, possible state of the universe). But this approach is highly disputed, because sometimes a very small change at a time t can have incredibly huge effects at a time later than t.
A final caveat: In all of the above, I have silently presumed that the correct semantics for (2) is the ordinary standard conditional, which is only false when the antecedent is true and the subsequent is false. However, this is only a highly idealized and rough approximation to the meaning of English if-then clauses.