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19 July, 03:26

Translate the following English sentence into logical expressions using the definitions above: (a) You drive over 65 miles per hour, but you do not get a speeding ticket. (b) If you do not drive over 65 miles per hour, then you will not get a speeding ticket. (c) You get a speeding ticket, but you did not drive over 65 miles per hour.

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  1. 19 July, 03:47
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    Logical expressions are expressions that connect two or more different sentences (prepositions) together in a way that they make grammatical sense. This is done by logical connectors.

    To answer the highlighted questions directly

    Let

    P: You drive over 65 miles per hour

    q: You get a speeding ticket

    ~P: You do not drive over 65 miles per hour

    ~q: You do not get a speeding ticket

    (a) p ∧ ~q

    (b) ~p→~q

    (c) q ∧ ~p
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