document.write( "Question 1010727: INSTRUCTIONS: Use natural deduction to derive the conclusion in the following problems.\r
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\n" ); document.write( "1. A ⊃ (Q ∨ R)
\n" ); document.write( "2. (R • Q) ⊃ B
\n" ); document.write( "3. A • ∼B
\n" ); document.write( "/ R ≡ ∼Q
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Algebra.Com's Answer #626591 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!
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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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