Discrete Mathematics with Graph Theory (3rd Edition) 4

# Discrete Mathematics with Graph Theory (3rd Edition) 4 - 2...

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2 Solutions to Exercises (c) [BB] True (the hypothesis is false). (d) False (hypothesis is true, conclusion is false). (e) [BB] False (hypothesis is true, conclusion is false: v'4 = 2). (0 True (g) [BB] True (h) True (i) EBB] True (the hypothesis is false: .fX2 = Ixl) G) True (k) [BB] False (I) True 5. (a) [BB] a 2 ~ 0 and a is a real number (more simply, a = 0). (b) x is not real or x 2 + 1 f:. 0 (more simply, x is any number, complex or real). (c) [BB] x f:. 1 and x f:. -1. (d) There exists an integer which is not divisible by a prime. (e) [BB] There exists a real number x such that n ::; x for every integer n. (0 (ab)c = a(bc) for all a, b, c. (g) [BB] Every planar graph can be colored with at most four colors. (h) Some Canadian is a fan of neither the Toronto Maple Leafs nor the Montreal Canadiens. (i) There exists x > 0 and some y such that x 2 + y2 ~ o. G) x :2: 2 or x ~ -2. (k) [BB] There exist integers a and b such that for all integers q and r, b f:. qa + r. (1) [BB] For any infinite set, some proper'subset
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## This note was uploaded on 11/08/2010 for the course MATH discrete m taught by Professor Any during the Summer '10 term at FSU.

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