# Fill in the ?'s for the two proofs

Anonymous

Question description

I. Give a conditional proof of the following argument:

1. G > (E > N)

2. H > (~N > E)

3. G, conditional assumption.

4. H, conditional assumption.

5. ~N > E, by modus ponens on 4, 2.

6. E > N, by modus ponens on 3, 1

7. ~N > N, by hypothetical syllogism on 5,6.

8. ~~N v N, by material implication on 7.

9. N v N, by double negation on 8.

10. N, by ??? on 9

11. H > N, by conditional proof from 4 -> 10.

12. G > (H > N), by conditional proof from 3 -> 11.

II. Give an indirect proof of the following argument:

1. S > (R ^ ~T)

2. (S ^ R) > (T v E)

3. Q v ~T) > ~E   /~S

4) S (assume opposite of conclusion)

5) (R ^ ~T) (4, 1, MT)

6) R (5, simplification)

7) (S ^ R) (4, 6, conjunction)

8) (T v E) (7, 2, MT)

9) ~T (5, simplification)

10) E (8, 9, ??)

11) (Q v ~T) (9, ??)

12) ~E (11, 3, MT)

13) (E ^ ~E) (10, 12, conjunction)

14.) ~S (??)

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