Question

If hypothesis `p` is false and conclusion `q` is false, the statement `q -> ~p` would be?

Answer 1

If your conclusion about your hypothesis is known to be false, then your conclusion is wrong about your hypothesis... and your hypothesis may very well be true.

Thus, even if you later come up with a true conclusion, it is, with regards to your hypothesis, inconclusive.

i.e. Your conclusion could have been true for any given hypothesis, not necessarily the one you're talking about.

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An example:

We falsely hypothesize that `"Na"` is a nonmetal, and falsely conclude that `"Na"` is a nonmetal.

(We know it is a metal.)

What if we had this:

We later realize and correctly conclude that `"Na"` is an element, and we, for some reason, believe that it proves that the hypothesis where sodium is a nonmetal is false.

Well, the fact that sodium is an element doesn't necessarily prove that the hypothesis is false. Any element can be a metal or otherwise.

Thus, our correct conclusion does not prove our hypothesis true or false.