In my philosophy class, where we cover theory of knowledge, I leaned about Gettier problem. Gettier's counterexample to JTB is following: From A has Ford which is justified false belief, B can deduct ,using inference rule such as $\vee $ intro, A has a Ford or C is in L.A. And C is really in L.A. Then B has a justified true belief "A has a Ford or C is in L.A." So, JTB is not a necessary condition of knowledge.
But, if we have a set of false thing, then we can deduce anything from the set. So, I asked my prof that Is there any relation between counter-factual conditional and an argument which has at least one false premise. But he replied that what we concern here is argument not conditional. And we could deduct anything from the set only if at least one of the element of it is contradiction.
But I need some more explanation about it.