Rules of Inference II - Answers

Instructions: For each of the following derivations, complete the justification by providing the rule of inference and line numbers.

A.

1. (A v B) ⊃ (C & D) premise
2. (A & C) premise
3. (C ⊃ D) premise
4. A simp 2
5. (A v B) disj 4
6. (C & D) m.p. 1,5
7. C simp 6
8. D simp 6

B.

1. (A ⊃ B) & ~C) premise
2. (~D v C) premise
3. (B ⊃ E) & ~E premise
4. ~C simp 1
5. ~D d.s. 2,4
6. (A ⊃ B) simp 1
7. (B ⊃ E) simp 3
8. (A ⊃ E) h.s. 6,7

C.

1. (E ⊃ F) & (R ⊃ ~C) premise
2. E premise
3. ~F & (C v (~C ⊃ L)) premise
4. F premise  
5. E v R disj 2
6. E ⊃ F simp 1
7. R ⊃ ~C simp 1
8. F v ~C disj 4
9. ~F simp 3
10. ~C d.s. 8,9
11. (C v (~C ⊃ L)) simp 3
12. ~C ⊃ L d.s. 10,11