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I'm in the process of learning fitch proofs and I've come across one I'm having trouble setting up.
Premise: ~(A > B)
Goal: (A & ~B)
In other words, it looks something like this:
1 | ~(A > B):PR
.
.
.
2 | A:... (I've achieved this much)
.
.
.
3 | ~B:?
4 |(A & ~B):&I 2,3
So far I've got logic for concluding A, but now I struggle to conclude ~B so that I can join the two.
How should I go about doing this?
So far I've got logic for concluding A, but now I struggle to conclude ~B so that I can join the two.
The subproofs for A and ~B are very similar in outline, with just a slight variation in details.
In each you derive a contradiction of the premise, ~(A>B), to discharge their assumptions (of ~A and B respectively) and derive their negations.
The deduction of that conditional, A>B, in each requires a Conditional Proof: Assume A so to derive B. It is just that these derivations for B are different.
In the first do so by explosion of the contradictory assumptions (ex falso quodlibet).
In the second, just reiterate : B is true under an assumption of B.
