(1) Is (p&or; q) &and; (¬p &or; r) ⟶ (q &or; r) a tautology (i.e., “always true”)? Please explain your answer. Note that ¬? denotes “not p” and ⟶ denotes “p implies q”. (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

(1) Is (p∨ q) ∧ (¬p ∨ r) ⟶ (q ∨ r) a tautology (i.e., “always true”)? Please explain your answer. Note that ¬? denotes “not p” and ⟶ denotes “p implies q”. (10%)

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