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Question 1209922: A. Use the first thirteen rules of inference to derive the conclusions of the following symbolized arguments:
1. (O v M) ⊃ S
2. ~S / ~M
1. ~(~E • ~N) ⊃ T
2. G ⊃ (N v E) /G ⊃
T
1. ~(F • A)
2. ~(L v ~A)
3. D ⊃ (F v L) /~D
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's derive the conclusions using the first thirteen rules of inference.
**Argument 1:**
1. (O v M) ⊃ S
2. ~S / ~M
3. ~(O v M) (Modus Tollens, 1, 2)
4. ~O • ~M (De Morgan's Theorem, 3)
5. ~M (Simplification, 4)
**Argument 2:**
1. ~(~E • ~N) ⊃ T
2. G ⊃ (N v E) / G ⊃ T
3. N v E (Double Negation, ~E • ~N)
4. G ⊃ ~(~E • ~N) (Hypothetical Syllogism, 2, 3)
5. G ⊃ T (Hypothetical Syllogism, 4, 1)
**Argument 3:**
1. ~(F • A)
2. ~(L v ~A)
3. D ⊃ (F v L) / ~D
4. ~L • ~~A (De Morgan's Theorem, 2)
5. ~L • A (Double Negation, 4)
6. A (Simplification, 5)
7. ~F v ~A (De Morgan's Theorem, 1)
8. ~F (Disjunctive Syllogism, 6, 7)
9. ~L (Simplification, 5)
10. F v L (Constructive Dilemma, 8, 9)
11. ~D (Modus Tollens, 3, 10)
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