Natural Deduction Homework #3

Do Natural Deductions for the following arguments:

(1) 1. W → M (2) 1. W

2. N → ~ M 2. (W & C) → (M & V)

3. N 3. C

\ ~ W 4. V → F

\ F

(3) 1. A → ~ B (4) 1. E → (T → S)

2. A & C 2. ~ (T → S)

\ ~ B 3. ~ R v E

\ ~ R

(5) 1. H → ~ B (6) 1. F → (G → H)

2. D → B 2. ~ F → J

3. H 3. ~ (G → H)

\ ~ D \ J

(7) 1. (A & E) → F (8) 1. A v C

2. E 2. B → ~ (A v C)

3. F → (D & ~ C) \ ~ B

4. A

\ ~ C

(9) 1. (D & H) → R (10) 1. ~ X → Y

2. S → (D & H) 2. Z → ~ X

\ S → R 3. Y → ~ V

\ Z → ~ V

(11) 1. (A & B) → ~ C (12) 1. ~ L & (J → K)

2. C v (D & E) 2. L v J

3. (A & B) & F 3. ~ I → ~ K

\ D & E \ I