Propositional Logic

Proof Construction:  Problem Set # 1
 

Problem # 1

1. C
D C

Problem # 2
1. E (F G)
F (E G)

Problem # 3
1. H (I J)
H  I

Problem # 4
1. N O
(N P) O

Problem # 5
1. (Q R) S
Q S

Problem # 6
1. T ~(U V)
T U

Problem # 7
1. W (X ~Y)
W (Y X)

Problem # 8
1. E F
2. E G
E (F G)

Problem # 9
1. H (I J)
2. ~I

H J

Problem # 10
1. (K L) ~(M N)
2. (~M ~N) (O P)
3. (O P) (Q R)


(L K) (R Q)

Problem # 11
1. S T
2. S T

T

Problem # 12
1. A (B C)
2. C (D E)

A (B D)

Problem # 13
1. E F
2. G F

(E G) F

Problem #14
1. [(H I) J] [~K (I ~J)]
H K

Problem # 15
1. [L (M N)] (M N)
L (M N)

Problem # 16
1. S (T U)
2. (T U) V
3. ~S (T U)
S V

Problem # 17
1. ~W [(X Y) (Z Y)]
2. W (X Z)
Y

Problem # 18
1. (A B) (C D)
2. ~A (E ~E)
3. ~C
~E

Problem # 19
1. (F G) (H I)
2. F H
3. (F ~I) (H ~G)
G ~I

Problem # 20
1. Q (R S)
2. (Q T) (T S)
S

Problem # 21
1. (U V) (W X)
(U W) (V X)

This is a very short proof with CP.
 

Problem # 22

1. (Y Z) (A B)

(Y A) (Z B)

This is another very short proof with CP.

Problem # 23
1. (C D) (E F)
2. G (C E)
G (D F)

Problem # 24
1. (H I) (J K)
2. H J
3. (H ~K) (J ~I)
4. (I ~K) L
5. K (I M)
L M