# I need to prove the validity of these problems by using the 18 proof rules.

**Question description**

(1) 1. ~M or N

2. ~R implies ~N/: M implies R

(2) 1. ~A implies (B and C)

2. ~C/: A

(3) 1. H implies K

2. C iff D

3. ~C implies ~K/: H implies D

(4) 1. (A and B) implies C

2. A and ~C/: ~B

(1) 1. (A and B) implies R

2. A

3. C implies ~ R/: ~(C and B)

(2) 1. ~H

2. H or K

3. L implies H

4. ~(K and ~L) or (~L and M)/:M

(3) 1. ~(D or C)

2. ~C implies (A implies ~B)

3. A iff B/: ~A

(4) 1. A or B

2. C

3. (A and C) implies D/: D or B

(5) 1. A implies B

2. A or (B and C)/: B

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