6. Simplify each of the following propositions, quoting the laws you use.
(a). (P ∧ Q) ∨
[
∼ (∼ P ∨ Q)
]
(b). (P ∨ Q) ∧
[
∼ (∼ P ∧ Q)
]
(c). ∼
[
∼ [(P ∨ Q) ∧ R]∨ ∼ Q
]
(d). [
(P =⇒ Q) ∨ (Q =⇒ R)
]
∧ (R =⇒ S)
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