Question: Please write out so I can copy and paste it*** Exercise 1.5.3: Using the laws of logic to prove tautologies. info About Use the laws

Please write out so I can copy and paste it***

Exercise 1.5.3: Using the laws of logic to prove tautologies.

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Use the laws of propositional logic to prove that each statement is a tautology.

(a)

(p q) (p r)

(b)

p (r p)

(c)

r (r p)

(d)

(p q) q

(e)

p (p q)

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