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5. Translate the sentences into propositional expressions: Only the fox can catch the hare if the hare is alert and quick. Let: P: The fox

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5. Translate the sentences into propositional expressions: "Only the fox can catch the hare if the hare is alert and quick." Let: P: The fox can catch the hare Q: The lynx can catch the hare. R: The hare is alert S: The hare is quick Write the translation in logic. b. "If (stay at the hotel and watch TV), you then must (go to the museum and spend some time there)". The parentheses are used to avoid ambiguity concerning the priority of the logical connectives P: You stay at the hotel. Q: You watch TV R: You go to the museum S: You spend some time in the museum Write the translation in logic. 6. Prove the following equivalence relations without making use of Truth Tables Note: A proposition that is always true is called "tautology" in logic

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