12. Use a direct proof to show that the following argument is valid. Need to add

Question

12. Use a direct proof to show that the following argument is valid.

Need to add the lines to finish the proof. The first box should be the proof, second two boxes should reference the line numbers, the last box should say which rule we are using. I have already written one line, I need to write the rest of the proof to find the answer. Thank you in advance!!

4 NJ 2 Simp 5 Check Modus Ponens MP Modus Tollens MT Hypothetical Syllogism HS Disjunctive Syllogism DS Constructive Dilemma CD Simplification Simp Conjunction Conj Addition Add Add Line X Delete Line Check Proof

Explanation / Answer

1. ~I · ~(W v X)
2. ~J · (Y ? ~Z)
3. ~J · ~I ) ? [(~I v B) ? (J v ~M)]
4. ~J ( 2 Simplification)
5. ~I ( 1 Simplification)
6. ~J · ~I (4,5 Conjunction)
7. (~I v B) ? (J v ~M)   (6, 3 MP)
8. ~I v B (1, Addition)
9. (J v ~M) (8, 7 MP)
10. ~M (9,4 Disjunctive Syllogism)
11. ~M · ~J (10,4 Conjunction)

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