Rules of Inference III - Answers

 

Instructions: Print out this page. 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 & B) premise
3. (C & D) ⊃ (L v M) premise
4. (A v B)  ⊃ (L v M) h..s. 1,3
5. ~A  simp 2
6. B simp 2
7. (A v B) disj 6
8. (L v M) m.p. 4,7

B.

1. (A ⊃ B) ⊃ ~C) premise
2. ((A ⊃ B) v B) premise
3. (B ⊃ E) premise
4. ~B premise
5. (~C v E) dil 1,2,3
6. (A ⊃ B) d.s. 1,4
7. ~B v E disj 4
8. (~B v E) & (B ⊃ E) conj 3,7
9. ~B & (~C v E) conj 4,5

C.

1. (E ⊃ ~F) & (R ⊃ C) premise
2. E & (~C ⊃ (L & ~P)) premise
3. (R & S) & (X ⊃ F) premise
4. E simp 2
5. (E ⊃ ~F)   simp  1
6. (R ⊃ C) simp 1
7.  (~C ⊃ (L & ~P)) simp 2
8. R & S simp 3
9. (X ⊃ F) simp 3
10. ~F m.p. 4,5
11. ~X m.t. 5,10