1. Complete the following derivations by entering justifications for the derived sentences:

a. Derive: A & B 1 A Assumption

2 A B Assumption

3 B

4 A & B

*b. Derive: ~ C

1 A (B & ~ C) Assumption

2 A & B Assumption

3 A

4 B & ~ C

5 ~ C

c. Derive: ~ (A ~ B)

1 ~ (A ~ B) (~ C ~ D) Assumption

2 A (~ D & C) Assumption

3 D & A Assumption

4 A

5 ~ D & C

6 ~ D

7 ~ C ~ D

8 ~ (A ~ B)

*d. Derive: (E & D) & (~ B & C)

1 ~ B (D & E) Assumption

2 (A & ~ B) & C Assumption

3 A & ~ B

e. Derive: F ~ G

1 (E H) (F ~ G) Assumption

2 (C D) (E & ~ H) Assumption

3 C Assumption

4 C D

5 E & ~ H

6 E

7 E H

8 F ~ G

*f. Derive: ~ G

1 (H & ~ I) ~ G Assumption

2 (F ~ G) H Assumption

3 F & ~ I Assumption

4 F

5 F ~ G

6 H

7 ~ I

8 H & ~ I

9 ~ G

g. Derive: D ~ B

1 (A & ~ B) C Assumption

2 (C D) (D ~ B) Assumption

3 ~ B & A Assumption

4 A

5 ~ B

6 A & ~ B

7 C

8 C D

9 D ~ B

*h. Derive: M & ~ N

1 (K & ~ L) & (~ I & J) Assumption

2 ~ L M Assumption

3 (K & ~ I) ~ N Assumption

4 K & ~ L

5 ~ L

6 M

7 K

8 ~ I & J

9 ~ I

10 K & ~ I

11 ~ N

12 M & ~ N