SOLUTION: use the inference rules, replacement rules, indirect proof and/or conditional proof to derive the conclusion. 1. F ⊃ ~U 2. ~F ⊃ P 3. F v ~F/~U v P

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Question 1171802: use the inference rules, replacement rules, indirect proof and/or conditional proof to derive the conclusion.
1. F ⊃ ~U
2. ~F ⊃ P
3. F v ~F/~U v P
Answer by Edwin McCravy(20065)   (Show Source): You can put this solution on YOUR website!
It's immediate if you can use Constructive Dilemma, which is this:
[(p ⊃ q) & (r ⊃ s) & (p v r)] ⊃ (q v s)   

But here's how to prove it WITHOUT using Constructive Dilemma.

 1. F ⊃ ~U
 2. ~F ⊃ P
 3. F v ~F  / ~U v P

            | 4. ~(~U v P)            Assumption for Indirect Proof
            | 5. ~~U & ~P             4, DeMorgan's Law
            | 6. U & ~P               5, Double Negation
            | 7. U                    6, Simplification 
            | 8. ~F                   1,7 Modus Tollens
            | 9. ~P & U               6, Commutation
            |10. ~P                   9, Simplification
            |11. ~~F                  2,10 Modus Tollens
            |12. F                    11, Double Negation
            |13. ~F & ~~F             12,11 Conjunction
            |14. ~F & F               13, Double Negation
            |15. ~(F v ~F)            14, DeMorgan's Law
            |16. (F v ~F) & ~(F v ~F) 3,15 Conjunction
17. ~U v P     Lines 4-16    Indirect Proof          

Edwin
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