SOLUTION: 1. I > ( L & W)
2. (~W > H) > S
/ I > S
3. ~I v (L & W) 1 MI
4. (~I v L) & (~I & W) 3 Dist.
Can anybody finish this logical proof for me? Thanks!
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Question 981858: 1. I > ( L & W)
2. (~W > H) > S
/ I > S
3. ~I v (L & W) 1 MI
4. (~I v L) & (~I & W) 3 Dist.
Can anybody finish this logical proof for me? Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You made a typo on line 4. It should be ~I v W instead of ~I & W
| Number | Statement | Lines Used | Reason |
|---|
| 1 | I > ( L & W) | | |
| 2 | (~W > H) > S | | |
| :. | I > S | | |
| 4 | ~I v (L & W) | 1 | Material Implication |
| 5 | (~I v L) & (~I v W) | 4 | Distribution |
| 6 | (~I v W) & (~I v L) | 5 | Commutation |
| 7 | ~I v W | 6 | Simplification |
| 8 | ~~I > W | 7 | Material Implication |
| 9 | I > W | 8 | Double Negation |
| 10 | ~(~W > H) v S | 2 | Material Implication |
| 11 | ~(~~W v H) v S | 10 | Material Implication |
| 12 | ~(W v H) v S | 11 | Double Negation |
| 13 | (~W & ~H) v S | 12 | De Morgan's Law |
| 14 | S v (~W & ~H) | 13 | Commutation |
| 15 | (S v ~W) & (S v ~H) | 14 | Distribution |
| 16 | S v ~W | 15 | Simplification |
| 17 | ~W v S | 16 | Commutation |
| 18 | ~~W > S | 17 | Material Implication |
| 19 | W > S | 18 | Double Negation |
| 20 | I > S | 9,19 | Hypothetical Syllogism |
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