Solutions to Argument Symbolization Exercises

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 /∴ ~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
The argument is also valid if step 1 is translated, "(T I) · 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)