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Use truth tables to verify the following logical equivalences. Include a few words of explanation with your answers. (a) p→q ≡ ∼p ∨ q The truth table shows that p → q and ∼p ∨ q always do not always have the same truth values. Therefore they are are not logically equivalent. (b) ∼(p → q) ≡ p ∧ ∼q. (b) ∼(p → q) ≡ p ∧ ∼q. The truth table shows that ∼(p → q) and p ∧ ∼q always do not always have the same truth values. Therefore they are are not logically equivalent.

Use truth tables to verify the following logical equivalences. Include a few words of explanation with your answers. (a) p→q ≡ ∼p ∨ q The truth table shows that p → q and ∼p ∨ q always do not always have the same truth values. Therefore they are are not logically equivalent. (b) ∼(p → q) ≡ p ∧ ∼q. (b) ∼(p → q) ≡ p ∧ ∼q. The truth table shows that ∼(p → q) and p ∧ ∼q always do not always have the same truth values. Therefore they are are not logically equivalent.

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Use truth tables to verify the following logical equivalences. Include a few words of explanation with your answers. (a) p→q ≡ ∼p ∨ q The truth table shows that p → q and ∼p ∨ q always do not always have the same truth values. Therefore they are are not logically equivalent. (b) ∼(p → q) ≡ p ∧ ∼q. (b) ∼(p → q) ≡ p ∧ ∼q. The truth table shows that ∼(p → q) and p ∧ ∼q always do not always have the same truth values. Therefore they are are not logically equivalent.

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