Construct a proof to show that the following claims are true.
a) R ↔ P, R → ¬ P ⊢ ¬ P
b) ¬ A → B, B → C, ¬ C ⊢ A
c) ¬ ( ¬ P v Q) ⊢ P
d) (A ˄ B) v P, P → ¬ A, A ˄ C ⊢ A ˄ B
e) A v B ⊢ ¬ (¬ A ˄ ¬ B)