SOLUTION: Hi could anyone help me with this proof?
1. V v H
2. ~(V & D)
3. ~(D & H)
/ ~(D & O)
Thank you!
Algebra.Com
Question 981101: Hi could anyone help me with this proof?
1. V v H
2. ~(V & D)
3. ~(D & H)
/ ~(D & O)
Thank you!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
| Number | Statement | Lines Used | Reason |
|---|
| 1 | V v H | | |
| 2 | ~(V & D) | | |
| 3 | ~(D & H) | | |
| :. | ~(D & O) | | |
| 4 | H v V | 1 | Commutation |
| 5 | ~~H v V | 4 | Double Negation |
| 6 | ~H -> V | 5 | Material Implication |
| 7 | ~V v ~D | 2 | De Morgan's Law |
| 8 | ~~V -> ~D | 7 | Material Implication |
| 9 | V -> ~D | 8 | Double Negation |
| 10 | ~H -> ~D | 6,9 | Hypothetical Syllogism |
| 11 | ~D v ~H | 3 | De Morgan's Law |
| 12 | ~~D -> ~H | 11 | Material Implication |
| 13 | D -> ~H | 12 | Double Negation |
| 14 | D -> ~D | 13,10 | Hypothetical Syllogism |
| 15 | ~D v ~D | 14 | Material Implication |
| 16 | ~D | 15 | Tautology |
| 17 | ~D v ~O | 16 | Addition |
| 18 | ~(D & O) | 17 | De Morgan's Law |
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