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# Construct derivations in SD to establish these claims: '(A B) (A B)' is a theorem in SD. {A (B C), A B, B C} is inconsistent in SD.

1. Construct derivations in SD to establish these claims:

a. ‘(∼A ≡ B) ⊃ (A ≡ ∼B)’ is a theorem in SD.

b. {A ⊃ (B ∨ ∼ C), ∼ A ⊃ B, ∼ B & C} is inconsistent in SD.

c. The following argument is valid in SD: A ⊃ (B ∨ ∼ C) B ⊃ (C & D) ∼ C ⊃ (∼ B & D) A ⊃ D

2. Show that ‘(A ∨ (B ∨ C)’ and ‘∼ A ⊃ (∼ B ⊃ C)’ are equivalent in SD+.