SOLUTION: Proof by Natural Deduction � Propositional Logic. Use a direct proof to show that the following argument is valid. Premise 1: (E � I) v (M �U) Premise 2: ~E Conclusion: ~(E

Question 1043570: Proof by Natural Deduction � Propositional Logic. Use a direct proof to show that the following argument is valid.

Premise 1: (E � I) v (M �U)
Premise 2: ~E
Conclusion: ~(E v ~M)
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
1) ~E --------------hypothesis
2) ~E v ~I -------------addition
3) ~(E�I) -------------de Morgan's
4) (E � I) v (M �U) ----hypothesis
5) ~(E � I) -> (M �U) --material implication on #4
6) M �U -----------modus ponens by #3 and #5
7) M ---------------simplification
8) ~E � M ----------conjunction, by #1 and #7
9) ~(E v M) -----------de Morgan's
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