SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use an ordinary proof (not conditional or indirect proof): 1. A &#8835; (Q &#8744; R)

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Question 1010727: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.
Use an ordinary proof (not conditional or indirect proof):
1. A ⊃ (Q ∨ R)
2. (R � Q) ⊃ B
3. A � ∼B
/ R ≡ ∼Q

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

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

SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use an ordinary proof (not conditional or indirect proof): 1. A &#8835; (Q &#8744; R)

SOLUTION: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems. Use an ordinary proof (not conditional or indirect proof): 1. A ⊃ (Q ∨ R)