SOLUTION: How would you prove this argument valid ? 1. A > H 2. G > S 3. ~ K

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Question 1140965: How would you prove this argument valid ?
1. A > H
2. G > S
3. ~ K > (A v G)
4. ~ K & D
5.( H v S)> J /J
Answer by math_helper(2461) (Show Source):
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How would you prove this argument valid ?
1. A > H
2. G > S
3. ~ K > (A v G)
4. ~ K & D
5.( H v S)> J /J
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1. A > H
2. G > S
3. ~ K > (A v G)
4. ~ K & D
5.( H v S)> J
6. ~K 4, SIMP
7. A v G 6,3 MP
8.:: A Conditional Proof (CP) assumption #1
9.:: H 8,1 MP
10.:: H v S 9 ADD
11.:: G CP assumption #2
12.:: S 12,2 MP
13.:: S v H 12 ADD
14.:: H v S 13 COMM
15.:: A v G --> H v S 8-14 Proof by Cases (PBC)
16. A v G --> H v S 8-15 CP
17. H v S 7,16 MP
15. J 17,5 MP

EDITED 5/15: Corrected line 17 from "5,16 MP" to "7,16 MP"

SOLUTION: How would you prove this argument valid ? 1. A > H 2. G > S 3. ~ K > (A v G) 4. ~ K & D 5.( H v S)> J /J