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Exercise 1.5.2: Using the laws of logic to prove logical equivalence.

Use the laws of propositional logic to prove the following:

(a)

p q q p

(b)

p (p q) p

(c)

(p q) (p r) p (q r)

(d)

p (q r) q (p r)

(e)

(p r) (q r) (p q) r

(f)

(p (p q)) p q

(g)

(p q r) (p q r) p r

(h)

p (p r) p r

(i)

(p q) r (p r) q