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1. C <-> T
2. ~C -> (~S v ~R)
3. ~C -> D
4. (~D v S) & (~D v R)
We have to show T
5. ~D v (S&R) Distributive law on 4
6. ~C -> ~(S&R) DeMorgan's law on the right side of 2
7. (S & R) -> C Contrapositive of 6
8. ~D -> C Contrapositive of 3
9. [(S&R) -> C} & (~D -> C) Conjunction of 7 and 8
10. [~(S&R) v C] & (~~D v C) Writing conditionals as disjunctions in 9
11. [~(S&R) v C] & (D v C) Double negation on D in 10
12. [~(S&R) & D] v C Distributive law on 11
13 ~[(S&R v ~D] v C DeMorgan's law on the left part of 12
14. (S&R) v ~D Commutative law on 5
15. [(S&R) v ~D] & { ~[(S&R) v ~D] v C } Conjunction of 14 and 13
16.{[(S&R) v ~D] & ~[(S&R) v ~D]} v C Associative law on 15
17. 0 v C The expression in braces in 16 is a contradiction
18. C The identity law for disjunction in 17
19. T By biconditional 1
Edwin
