If you are allowed to use the LEM, then this is easy. Do a disjunction elimination on A V ~A and then on B V ~B. In each of the four possibilities it is easy to derive the necessary conclusion.
Good evening everyone,
With regards to ((A & B) V nA) V nB, I found this sentence to be a tautology, where the LEM applies. I am trying to create a formal proof in Fitch to show that it is indeed a tautology, but don't know which direction to go in.
Any help is greatly appreciated. Thank you
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& represents the conjunctive
V the disjunctive
n is negation
Hi emakarov,
Thank you for that hint. I can obtain the same conclusions from the A and nA subproofs, as well as the B and nB ones, but I can't figure out how to link them together properly.
Here is where I am stuck:
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I'm sure it's something really simple, I'm just at a block!
Thank you
You need to do \/E on B \/ ~B inside the \/E on A \/ ~A.
Code:1. A \/ ~A LEM 2. A Hyp 3. B \/ ~B LEM 4. B Hyp 5. A /\ B /\I: 2, 4 6. (A /\ B) \/ ~A \/I: 5 7. ((A /\ B) \/ ~A) \/ ~B \/I: 6 8. ~B Hyp 9. ((A /\ B) \/ ~A) \/ ~B \/I: 8 10. ((A /\ B) \/ ~A) \/ ~B \/E: 4-7, 8-9, 3 11. ~A Hyp 12. (A /\ B) \/ ~A \/I: 11 13. ((A /\ B) \/ ~A) \/ ~B \/I: 12 14. ((A /\ B) \/ ~A) \/ ~B \/E: 2-10, 11-13, 1