MATH 151 Lecture 2: September 14th - 1.2-4 Venn Diagrams and Multiplication Principle

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A fundamental principle of counting: is a set a contains precisely k elements, we say a has size. A = {2, 4, 6, 8} n(a) = 4. For two sets: n(aub) = n(a) + n(b) n(anb) For three sets: n(aubuc) = n(a) + n(b) + n(c) n(anb) n(anc) n(bnc) + n(anbnc) In a survey of 200 university students, 62 were taking astronomy, 98 were taking biology, 75-27 = 48 n(a) + n(b) + n(c) = 8+10+57 = 75. Let a and b be sets in u where n(u) = 300, n(a) = 100, n(b) = 120, n(anb) = 60. Ex. n(u) = 100, n(a) = 30, n(b) = 20, n(c) = 29, n(aub) = 37, n(auc) = 43, n(buc) = 34, n(aubuc) = 45. 1. 4 the multiplication principle: n(aub) = n(a) + n(b) n(anb) X = 13: n(auc) = n(a) + n(c) n(anc) X = 16: n(buc) = n(b) + n(c) n(bnc)

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