Propositional Logic

Proof Construction:  Problem Set # 2

Problem # 1

 1. (S · U) → P 2. (U → P) → W 3. S ∴ W

Problem # 2

 1. A ▼ (B · C) 2. (A ▼ B) → D ∴ C ▼ D

Problem # 3

 1. G → (B → C) 2. G · ~C 6. ~B ∴ ~B

Problem # 4

 1. P → S ∴ P → (H → S)

Problem # 5

 1. (F → R) · (L → U) 2. (U · R) → C 3. ~C ∴ ~F ▼ ~L

Problem # 6

 1. (~A ▼ B) · (A → C) 2. B → (C → E) ∴A → E

Problem # 7

 1. A → (B · C) 2. (B ▼ C) → I ∴ A → I

Problem # 8

 1. [(E · S) → P] · [(E · ~S) → ~P] ∴ E → [(S · P) ▼ (~S · ~P)]

Problem # 9

 1. A → (B ▼ C) 2. B → C ∴A → C

Problem # 10

 1. (A ▼ B) → (C · E) ∴ A → C

Problem # 11

 1. (P ▼ W) → (R · A) 2. (R → J) · ~J ∴ ~P

Problem # 12

 1. P → (C → N) 2. (N · R) → E 3. T → (R · ~E) ∴ P → (C → ~T)

Problem # 13

 1. T ▼ (I · O) 2. T → O ∴O

Problem # 14

 1. R ▼ N 2. R → G 3. G → ~S 4. (N → B) · (B → ~S) 5. S ▼ C ∴ C

Problem # 15

 1. P → S 2. S → ~(B · D) 3. (~B → T) · ~T 4. D ∴~P

Problem # 16

 1. (S → E) · (H → L) 2. (E ▼ L) → C 3. ~C ∴ ~(S ▼ H)

Problem # 17

 1. (T → E) · (A → L) ∴ (T · A) → (E · L)

Problem # 18

 1. E → S 2. E → (S → N) 3. S → (N → F) ∴ E → F

Problem # 19

 1. A → (B ▼ C) 2. E → (C ▼ P) 3. ~C ∴ ~(B ▼ P) → ~(A ▼ E)

Problem # 20

 1. (A ▼ B) → [(C ▼ E) → (~P · V)] 2. (~P ▼ ~N) → U ∴ A → (C → U)

Problem # 21

 1. (S ▼ ~S) → A ∴ A