Proofs V

Construct proofs for each of the following arguments using all the resources at your disposal.  Use the general-purpose proof form or do them on paper.

1. H ⊃~S, (~H v ~S)  F, F ⊃ B ///B
2. ~A ⊃ B, A ⊃ E, B ⊃ S, (E v S) ⊃ X /// X
3. P ⊃ Q, (~Q ⊃ ~P) ⊃ S, F ⊃ ~S //// ~F
4. H ⊃ S, ~P ⊃ ~S  /// H ⊃ P
5. A ⊃ B, A ⊃ ~B, ~A ⊃ G  ///G
6. (P v P) ⊃ S, ~(~P v (Q & ~R)) /// S
7. B ≡ G, (B& G) ⊃ Z, (~B & ~G) ⊃ Z /// Z
8. A ⊃ B, A ⊃ ~B /// ~A
9. ~A ⊃ S, ~E ⊃ S, ~(A & E)  ///S v H
10. A ⊃ B, B ⊃ ~A,  A v B /// A ⊃ (B ⊃ E)
11. P  ⊃ (Q ⊃ R), R ⊃ (Q  ⊃ S) ///P  ⊃ (Q  ⊃ S)
12. A  ⊃ B, (A& B)  ⊃ Q, (H&Q)  ⊃ S /// A ⊃ (H ⊃ S)
13. (C ≡ D) & ~(~D v E), C ⊃ (E v (F ⊃ ~G), (H ⊃ G) & F    /// ~H
14. ~(E ⊃ F), ~D ≡ E, ~A ⊃ D  /// (A v B) & (A v C)
15. ~F v C, G v D, ~F ⊃ ~G  /// C v D

Prove the following theorems:

1. ~[(A ⊃ ~A) & (~A ⊃ A)]
2. [~(~A & ~B) & ~A]  ⊃ B
3. [A & (B v ~A)]  ⊃ ~~B
4. [~A ⊃ (B & C)] ≡ [(A v B) & (A v C)]
5. A ⊃ (~A ⊃ ~B)