Question: Students are welcome to work together, but should write up solutions independently. All responses should include your reasoning. Homework may be submitted through the course

Students are welcome to work together, but should write up solutions independently. All responses should include your reasoning. Homework may be submitted through the course Moodle as a pdf file. 1. In each item, a statement is given. (It might be true or false.) For each item, find statements P and Q so that the statement is logically equivalent to "If P, then Q.\" (You do not need to prove the logical equivalence.) Ex: Every rose has a thorn. Solution. This is equivalent to \"If r is a rose, then r has a thorn." P : \"r is a rose.\" Q : "7' has a thorn." D (a) The cube of an even integer is divisible by 8. (b) Every cowboy sings a sad sad song. (c) Quadratic polynomials have at most two roots. (d) No man is an island. (e) It rains whenever I walk to school. (f) All speckled fandangoes have orange feathers

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