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Unformatted text preview: MATH 135 Winter 2009 Assignment #2 Due: Wednesday 21 January 2009, 8:20 a.m. Hand-In Problems 1. Express each statement as a logical expression using quantifiers. State the Universe of discourse. (a) There is a smallest positive integer. (b) There is no smallest positive real number. (c) Every integer is the sum of two integers. (d) Every pair of integers has a common divisor. (e) There is a real number x such that, for every real number y, y 2 y = x . (f) For every real number y , there is a real number x such that x 3 + x = y . (g) The equation x 3 + y 3 = z 3 has no positive integer solutions. 2. Write down the converse and contra positive of each statement. (a) If x > 3, then x 2 > 9. (b) If x greaterorequalslant 0 and xy greaterorequalslant 0, then y greaterorequalslant 0. 3. Throughout this problem, the universe of discourse is Z- the integers. (a) Is x y, x lessorequalslant y true or false? Explain....
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