Logic Homework for Wednesday 3/15

Do Natural Deductions for the following arguments:

Two Steps

(1) 1. D → E (2) 1. P & Q (3) 1. Y → Z

2. D & E 2. R 2. Y

\ E \ P & R \ Y & Z

(4) 1. D → E (5) 1. (K → L) → M (6) 1. J v ~ K

2. (E → F) & (F → D) 2. ~ M & ~ (L → M) 2. K v (L → J)

\ D → F \ ~ (K → L) 3. ~ J

\ L → J

Three Steps

(7) 1. (D & E) → (F & G) (8) 1. Q → R (9) 1. T → U

2. D 2. R → S 2. V v ~ U

3. E 3. ~ S 3. ~ V & ~ W

\ F \ ~ Q & ~ R \ ~ T

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

2. Z → X 2. C v D 2. K v H

3. ~X 3. A 3. ~ K

\ Y & ~ Z 4. B \ I

\ D