Unformatted text preview: J = 71, IB n ci = ll~~O J = 66, IB n DI = llg~O J = 47, IC n DI = ll~~O J = 28, IA n B n 01 = ll~gO J = 33, IA n B n DI = ll~gO J = 23, IA n C n DI = ll~gO J = 14, IB n C n DI = l \~050 J = 9, IA n B n C n DI = l1201000 J = 4. SO IA U B U C U DI = 772. Our answer is 1000  772 = 228. (b) Now 1 and 1000 must be excluded. Since 1 is not divisible by 2, 3, 4 or 7 while 1000 is divisible by 5, the answer is 228  1 = 227. 15. Let A, B, C, D be the sets of integers between 1 and 10,000 which are divisible by 3, by 5, by 7, and by 11, respectively. We have IAI = llO~OO J = 3333, IBI = llO~OO J = 2000, ICI = llO~OO J = 1428, IDI = llOlOlOO J = 909, IA n BI = l10 1 5 00 J = 666, IA n 01 = llO~lOO J = 476, IA n DI = ll030300 J = 303, IB n CI = ll030500 J = 285, IB n DI = llO~500 J = 181, IC n DI = llO~~O J = 129, IA n B n CI = ll~g~O J = 95, IA n B n DI = ll~~~O J = 60, IA n C n DI = llg~~O J = 43, IB n C n DI = ll~~~O J = 25, IA n B n C n DI = l \°1°5°5° J = 8....
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 Summer '10
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 Graph Theory, Integers, Sets

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