document.write( "Question 1155133: Use an ordinary proof (not conditional or indirect proof):
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Algebra.Com's Answer #777699 by jim_thompson5910(35256) $\"\"$ $\"About$

You can put this solution on YOUR website!

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Number	Statement	Line(s) Used	Reason
1	K v (S & N)
2	~(K & ~Q)
3	~(N & ~Q)
Conclusion	Q
4	(K v S) & (K v N)	1	Distribution
5	(K v N) & (K v S)	4	Commutation
6	K v N	5	Simplification
7	~K v ~~Q	2	De Morgan’s Law
8	~K v Q	7	Double Negation
9	~N v ~~Q	3	De Morgan’s Law
10	~N v Q	9	Double Negation
11	K -> Q	8	Material Implication
12	N -> Q	10	Material Implication
13	(K -> Q) & (N -> Q)	11,12	Conjunction
14	Q v Q	13,6	Constructive Dilemma
15	Q	14	Tautology

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