SOLUTION: Solve the following proof using natural deduction (rules of replacement and rules of implication).
1. D v Y
2. Y ⊃ ~(Z ⊃ D)
/ Y ≡ ~D
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Question 1029804: Solve the following proof using natural deduction (rules of replacement and rules of implication).
1. D v Y
2. Y ⊃ ~(Z ⊃ D)
/ Y ≡ ~D
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
1. D v Y --------------------Hypothesis
2. ~~D v Y --------------------double negation
3. ~D ⊃ Y ---------------------material implication
4. Y ⊃ ~(Z ⊃ D) ---------------hypothesis
5. Y ⊃ ~(~Z v D) --------------M.I.
6. Y ⊃ (Z & ~D) ---------------double neg. and deMorgan's law
7. ~Yv(Z & ~D) ----------------M.I.
8. (~Y v Z)&(~Y v ~D)-----------distributivity
9. ~Y v ~D -------------------simplification
10. Y ⊃ ~D -------------------M.I.
11. (~D ⊃ Y)&(Y ⊃ ~D) ---------conjunction on #3 and #10
12. Y ≡ ~D -------------------- #11 and logical equivalence for ≡
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