Math 141H-copyright Joe Kahlig, 10C Page 1Section 6.2: Venn DiagramsExample: If A = { 1, 3, 5} and B = {3, 4, 5, 6} compute the following.n(A) =n(B) = n(A ∩ B) = n(A ∪ B) =Union Formulas:Example: Suppose we survey 60 shoppers about two products: A and B.30 shoppers bought product A20 shoppers bought product B9 shoppers bought product A and product BA) Fill in a Venn Diagram that represents this information.B) How many shoppers bought product A but not B?C) How many shoppers bought product A or B?D) How many shoppers bought at least one product?E) How many shoppers bought exactly one product?F) How many shoppers bought neither of these products?Math 141H-copyright Joe Kahlig, 10C Page 2Example: If n(U ) = 500 and n(A ∪ B) = 300, what is n(Ac∩ Bc)?Example: Supposed we poll 100 people with 3 yes/no questions.22 people answered no to all three questions.45 answered yes to question 1.25 answered yes to question 2.32 answered yes to question 3.6 answered yes to only question 1 and question 3.12 answered yes to question 2 and question 3.2 answered yes to all three questions.A)Fill in a Venn Diagram that represents this information.B) How many people answered yes to question 2 or question 3?C) How many people answered yes to at most one question?D) How many people answered yes to question 2 but not question 1?E) How many people answered yes to exactly 2
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