(2) Please prove that (p ∨ ¬q) ∧ (¬p ∨ q) and (¬q ∧ ¬p) ∨(p ∧ q) are logically equivalent by using only laws of propositional logic. (10%)

四、Paul has two coolers. Cooler 1 contains 8 cans of cola and 3 cans of lemonade. Cooler 2 contains 5 cans of cola and 7 cans of lemonade. Paul randomly selects one can from Cooler 1 and transfers it into Cooler 2. Subsequently, Betty randomly selects two cans from Cooler 2. Given that both of Betty's selections are cans of cola, what is the probability that the can Paul initially transferred was lemonade? (10%)

題組內容

(2) Please prove that (p ∨ ¬q) ∧ (¬p ∨ q) and (¬q ∧ ¬p) ∨
(p ∧ q) are logically equivalent by using only laws of propositional logic. (10%)

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