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Unformatted text preview: (a) This part asks for IA U S U GI. IAuSuGI IAI + lSI + IGI  IA n SI  IA n GI  IS n GI + IA n S n GI 200 + 95 + 120 25 55  40 + 5 = 300 (b) This part asks for IS " (A U G)I = lSI  IS n (A U GI. Now S n (A U G) = (S n A) U (S n G), so Isn (AU G)I IS n AI + IS n GII(S n A) n (S n G)I IS n AI + IS n GI  IS nAn GI = 25 + 40 5 = 60. Therefore, IS" (A U GI = 95 60 = 35. 5. Let P, G, and 0 denote the sets of children who purchased popsicles, gum, and candy bars, respectively. The number of children present was at least IP U G U 01 = IPI + IGI + 101  IP n GI  IP n 01  IG n 01 + IP n G n 01 = 10 + 7 + 12 5 6 2 + IP n G n 01 = 16 + IP n G n 01 ;::: 16. Since there were only 15 children in all, the numbers don't tally. 6. Let E be the set of students taking English and M the set of students taking Math. (a) We want IE n MI. Now I(E U M)CI = 12, so IE U MI = 82 12 = 70. Since IE U MI = lEI + IMI  IE n MI, IE n MI = lEI + IMI  IE U MI = 59 + 46 70 = 35....
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 Summer '10
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 Graph Theory

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