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)

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Question 970141: 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 AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!

 1.	A ⊃ (Q ∨ R)	
 2.	(R • Q) ⊃ B	
 3.	A • ∼B	
/ R ≡ ∼Q

 4.     A              simplification,3
 5.    ~B              simplification,3
 6.  ~B ⊃ ~(R • Q)     contrapositive,2
 7. ~(R • Q)           modus ponens,6,7
 8.  ~R ∨ ~Q           deMorgan's,7
 9 .  R ⊃ ~Q           writing a disjunction as a conditional,8 
10.   Q ∨ R            modus ponens,1,4      
11. ~~Q ∨ R            double negation,10
12.  ~Q ⊃ R            writing a disjunction as a conditional,11
13. R ≡ ∼Q             definition of equivalence, 9,12 

Edwin