Use truth tables to determine whether the following pairs of symbolized statements are logically equivalent, contradictory, consistent, or inconsistent. First, determine whether the pairs of propositions are logically equivalent or contradictory; then, if these relations do not apply, determine if they are consistent or inconsistent.

1. ∼­D ∨ B…………………………..∼­(D ∙­ ­B)

2. F ∙­ M……………………………..∼­(F ∨ M)

3. ∼­K ⊃ L…………………………..K ⊃ ∼ ­L

4. R ∨ ∼­S……………………………S ∙ ∼­ ­R

5. ­∼ A ≡ X…………………………..(X ∙­ ∼ ­A) ∨ (A ∙ ∼ ­X)

6. H ≡ ­∼ G…………………………..(G ∙­ H) ∨ (∼­G ∙ ∼­ ­H)

7. (E ⊃ C) ⊃ L………………………E ⊃ (C ⊃ L)

8. N ∙­ (A ∨ ­∼E)……………………... ∼­A ∙ ­(E ∨ ∼ ­N)

9. M ⊃ (K ⊃ P)………………………(K ∙­ M) ⊃ P

10. W ≡ (B ∙­ T)………………………W ∙­ (T ⊃ ∼ ­B)

11. G ∙­ (E ∨ P)………………………∼ ­(G ∙­ E) ∙ ∼ ­(G ∙ P)

12. R ∙­ (Q ∨ S)……………………...(S ∨ R) ∙­ (Q ∨ R)

13. H ∙­ (K ∨ J)……………………….(J ∙­ H) ∨ (H ∙­ K)

14. Z ∙­ (C ≡ P)……………………….C ≡ (Z ∙ ∼ P)

15. Q ⊃ ­∼ (K ∨ F)………………….(K ∙ Q) ∨ (F ∙­ Q)