Proofs IV

Construct proofs for each of the following arguments using conditional proof or indirect proof.  You may use the General Purpose Proof Form for PL or do proofs the good old-fashioned way.

Use conditional proof:

1. A /// (E ⊃ E)
2. C ⊃ (D v E), ~(D v F) /// C ⊃ (E v G)
3. [P v (~S v ~Q)] ⊃ ~R ///~R v S
4. (Q v S), (P ⊃ ~Q), (P v R) /// ~R ⊃ S
5. (A & B) ≡ C,  A  ⊃ B /// A ≡ C
6. A /// (B ⊃ C) ⊃ ((A ⊃ B) ⊃  C)
7. (A ⊃ B) & (B ⊃ D) /// (A & B) ⊃ (C v D)
8. B ⊃ (~S v D), ~L v S, B ⊃ L  ///B ⊃ D

Use indirect proof:

1. (A & B) ⊃ (D v C), E ⊃ A, E v (A & B) /// A v (D v C)
2. ~A ≡ B, ~(A v E) /// B
3. M  ⊃ (~S  ⊃ U), (M  ⊃ S) ⊃ U /// U
4. ~(S  ⊃ ~T), (L v (R & ~S) /// L
5. L  ⊃ (R & S)   /// (~S  ⊃ ~L)