SOLUTION: Can i please have help solving these proofs?
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R Q) ⊃ B
3. A
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Question 1010046: Can i please have help solving these proofs?
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R Q) ⊃ B
3. A ∼B / R ≡ ∼Q
a regular proof to derive the conclusion of the following argument:
1. (A & U) < > ~R
2. ~(~R v ~A) / ~U
a regular proof to derive the conclusion of the following argument:
1. X >Y
2. (Y v ~X) > (Y > Z) / ~Z > ~X
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started
| Number | Statement | Lines Used | Reason |
|---|
| 1 | A -> (Q v R) | | |
| 2 | (R & Q) -> B | | |
| 3 | A & ~B | | |
| :. | R = ~Q | | |
| 4 | ~B & A | 3 | Commutation |
| 5 | A | 3 | Simplification |
| 6 | ~B | 4 | Simplification |
| 7 | Q v R | 1,5 | Modus Ponens |
| 8 | ~(R & Q) | 2,6 | Modus Tollens |
| 9 | ~R v ~Q | 8 | De Morgan's Law |
| 10 | R -> ~Q | 9 | Material Implication |
| 11 | ~~Q v R | 7 | Double Negation |
| 12 | ~Q -> R | 11 | Material Implication |
| 13 | (R -> ~Q) & (~Q -> R) | 10,12 | Conjunction |
| 14 | R = ~Q | 13 | Material Equivalence |
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