Question

Use Fitch to construct formal proofs for the following arguments. In two cases, you may find yourself re-proving an instance of the law of Excluded Middle, PV¬P, in order to complete your proof. If you've forgotten how to do that, look back at your solution to Exercise 6.33 in Language Proof and Logic 2nd Edition. Alternatively, with the permission of your instructor, you may use TAUT Con to justify an instance of Excluded Middle.

(P->Q)<->(¬PVQ)

Answer 1

If your instructor does not allow taut con then you can replace this step by proof of P ∨ ¬P.

1 2. P Q 3. P v -P Taut Con: 4. P Rule? 5. -P v Q 6 -P 7. -P v Q Rule?: 8. P v Q vElim: 6-7,4-5,3 9. P vQ 10. P 11. P Rule?: 12. Q 13. Q 14. Q vElim: 13-13,11-12 Intro: 10-14 15. P Q Intro: 2-8,9-15 16. (P Q)(-P v Q)