Propositional Logic

Proof Construction:  Problem Set # 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