4. Show using a truth table that ((p q)^(qr)) (pr) is a tautology. Justify your answer....

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4. Show using a truth table that ((p q)^(qr)) (pr) is a tautology. Justify your answer. 5. Use a truth table to verify p A (pV q) = p. Justify your answer. 6. Give a proof that (p-q)^(pr) and p (q^r) are logically equivalent without using truth tables. You can assume the "common logical equivalences" from the formula sheet and rule C1: that is logically equivalent to - V for all logical expressions and . Each time you use an equivalence rule provide the name or abbreviation of the rule. 7. Prove that (q (p-q)) p is a tautology using propositional equivalence rules. Each line of your proof should include an equivalent logical formula and a reason (give the name or abbreviation of the equivalence rule used). 4. Show using a truth table that ((p q)^(qr)) (pr) is a tautology. Justify your answer. 5. Use a truth table to verify p A (pV q) = p. Justify your answer. 6. Give a proof that (p-q)^(pr) and p (q^r) are logically equivalent without using truth tables. You can assume the "common logical equivalences" from the formula sheet and rule C1: that is logically equivalent to - V for all logical expressions and . Each time you use an equivalence rule provide the name or abbreviation of the rule. 7. Prove that (q (p-q)) p is a tautology using propositional equivalence rules. Each line of your proof should include an equivalent logical formula and a reason (give the name or abbreviation of the equivalence rule used).