1. K∨(S • N)
2. ∼(K •∼Q)
3. ∼(N •∼Q) / Q
4. ~K∨~~Q 2, DeMorgan's law
5. ~K∨Q 4, Double negation
6. ~N∨~~Q 3, DeMorgan's law
7. ~N∨Q 6, Double negation
8. Q∨~K 5, Commutation
9. Q∨~N 7, Commutation
10. (Q∨~K)•(Q∨~N) 8,9, Conjunction
11. Q∨(~K•~N) 10, Distribution
12. Q∨~(K∨N) 11, DeMorgan's law
13. (K∨S)•(K∨N) 1, Distribution
14. (K∨N)•(K∨S) 13, Commutation
15. K∨N 14, Simplification
16. ~~(K∨N) 15, Double negation
17. ~(K∨N)∨Q 12, Commutation
18. Q 17,16, Disjunctive syllogism
Edwin
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