Use truth tables to verify that each of the following is a tautology. Parts (a) and (b) are called commutative laws, parts (c) and (d) are associative laws, and parts (e) and (f) are distributive laws
(a) ( p ∧ q) ⇔ ( q ∧ p)
(b) ( p ∨ q) ⇔ ( q ∨ p)
(c) [ p ∧ ( q ∧ r)] ⇔ [( p ∧ q) ∧ r]
(d) [ p ∨ ( q ∨ r)] ⇔ [( p ∨ q) ∨ r]
(e) [ p ∧ ( q ∨ r)] ⇔ [( p ∧ q) ∨ ( p ∧ r)]
(f ) [ p ∨ ( q ∧ r)] ⇔ [( p ∨ q) ∧ ( p ∨ r)]
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