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) About Me  (Show Source):
You can put this solution on YOUR website!

I'll do the first one to get you started

NumberStatementLines UsedReason
1A -> (Q v R)
2(R & Q) -> B
3A & ~B
:.R = ~Q
4~B & A3Commutation
5A3Simplification
6~B4Simplification
7Q v R1,5Modus Ponens
8~(R & Q)2,6Modus Tollens
9~R v ~Q8De Morgan's Law
10R -> ~Q9Material Implication
11~~Q v R7Double Negation
12~Q -> R11Material Implication
13(R -> ~Q) & (~Q -> R)10,12Conjunction
14R = ~Q13Material Equivalence