Originally Posted by

**johnnyboy1** all 18 inference rules. yep, • is a conjunction. (i.e Mary went shopping and Gary played video games = M • G)

I got the last 2 questions btw:

(Q v ~T) v S, ~Q v (T • ~Q) : T ⊃ S

1. (Q v ~T) v S; Premise

2. ~Q v (T • ~Q); Premise

3. Q v (~T v S); 1 Association

4. Q v (T ⊃ S); 3 Implication

5. (~Q v T) • (~Q v ~Q); 2 Distribution

6. ~Q v T; 5 Simplification

7. ~Q v ~Q; 5 Simplification

8. ~Q; 7 Tautology

9. T ⊃ S; 4, 8 Disjunctive Syllogism

(C v B) -> (T & L), ~C -> (K -> ~K), ~T : ~K

1. (C v B) -> (T & L) : Premise

2. ~C -> (K -> ~K) : Premise

3. ~T : Premise

4. ~T v ~L : 3 Addition

5. ~(T & L) : 4 DeMorgan's Theorem

6. ~(C v B): 1, 5 Modus Tollens

7. ~C & ~B : 6 DeMorgan's Theorem

8. ~C : 7 Simplification

9. ~B : 7 Simplification

10. K -> ~K : 2, 8 Modus Ponens

11. ~K v ~K : 10 Implication

12. ~K : 11 Tautology

Thanks for the help emakarov and Piper