MATH 300 Midterm: MATH 300 UW 300 Su11 Midterm Solution
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Math 300, section c, summer 2011, solutions to midterm exam: for the following statements decide if the statement is true or false. If false, give a counter example. (a) x r y r z r xz = y. The true statement is its negation: x r y r z r xz 6= y. Let x = 0 and y = 1. Then for any z, xz = 0 6= 1. (b) (cid:2)(cid:0)y2 4y + 3 < 0(cid:1) (y z)(cid:3) = y = 2. Assume y2 4y+3 < 0 and y z. Then, from the rst equation we get that (y 1)(y 3) < 0. Since the product is negative, one of the factors must be negative and the other must be positive. But, y is an integer so y must be 2. (c) let x and y be integers. Then, xy is odd if and only if x and y are odd.
