Natural Deduction Homework #2

Do Natural Deductions for the following arguments:

Two Steps

(1) 1. D → E (2) 1. P & Q

2. D & F 2. R

\ E \ P & R

(3) 1. Y → Z (4) 1. D → E

2. Y 2. (E → F) & (F → D)

\ Y & Z \ D → F

(5) 1. (K → L) → M (6) 1. J v ~ K

2. ~ M & ~ (L → M) 2. K v (L → J)

\ ~ (K → L) 3. ~ J

\ L → J

Three Steps

(7) 1. (D & E) → (F & G) (8) 1. Q → R

2. D 2. R → S

3. E 3. ~ S

\ F \ ~ Q & ~ R

(9) 1. T → U (10) 1. ~ X → Y

2. V v ~ U 2. Z → X

3. ~ V & ~ W 3. ~X

\ ~ T \ Y & ~ Z

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

2. C v D 2. K v H

3. A 3. ~ K

4. B \ I

\ D