Finite Mathsection 6.2 Counting elements in a subsetNotation: n(A) = number of elements in set A.Term: Venn DiagramEx1, Let A = x x = 3k where k , x 10 Find n(A). −Ex2, Let B = x x = 3k where k , k 10 Find n(B) −Thm (Inclusion Exclusion Principle) (a) Given 2 sets A and B, n(A B) = n(A) + n(B) n(A B)∪∩ (b) Given 3 sets A, B, C, n(A B C) = n(A)+n(B)+n(C) n(A B) n(B C) n(A C) +n(A B C)∪∪ ∩∩∩ ∩∩Ex3, Let A = 1, 2, 3, 4 , B = 3, 4, 5, 6, 7 , C = 2, 9 , universal set U = n n , n 10 − Draw a Venn Diagram. Find (a) n(A) (b) n(B) (c) n(A B) (d) n(A B) (e) n(A ) (f) n(A B)∩∪ ∩'' (g) n(B C) (h) n(B C) (i) n(A B C) (j) n(A B C) (k) n(A B C )∪ ∩ ∪∪ ∩∩ ∩∩'Ex4, If n(A) = 7, n(B) = 8, and n(A B) = 5, evaluate n(A B).∩∪Ex5, If n(A) = 9, n(A B) = 5, and n(A B) = 15, evaluate n(B).∩∪Ex6, Let M = x x = 3k where k , x 200 , M = x x = 4k where k , x 20034 −Ÿ −Ÿ and M = x x = 6k where k , x 200 , M = x x = 9k where k , x 20069 −Ÿ −Ÿ Find (a) n(M ) (b) n(M ) (c) n(M M ) (d) n(M M ) 3 4 34 34∩∪ (e) n(M ) (f) n(M ) (g) n(M M ) (h) n(M M ) 6 9 69 69∩∪ (h) n(M M ) (i) n(M M ) (j) n(M M ) (k) n(M M )36 36 49 49∩∪ ∩
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