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From the adjoining figure list the elements of the different set operations: use commas and list alphabetically a) ξ = (b) A = (c) B' = (d) (A ∩ B) = { { { { } } } } If A and B are two sets such that A ∪ B has 50 elements. A has 12 elements and B has 45 elements. How many elements does A ∩ B have? How many elements does the the complement of A ∩ B have? If n(A) = 40, n(B) = 51 and n(A ∩ B) = 25 From the above sets find n(A - B) Find n(A ∪ B): n(A ∪ B) = n(A-B) = There are 80 teachers in a school. 50 teach science, 45 teach humanities, 15 teach both science and humanities. Find the number of teachers who teach: (a) science but not humanities. (b) Humanities but not science. (c) Humanities or science. In a group, 30 persons like tea or coffee, of these 15like tea and 6 like both coffee and tea. How many likecoffee? In a survey of 30 students in a class, 15 were fond ofhaving pineapple juice, 19 were fond of orange juice and 12 liked to have both pineapple as well as orange juice. Find how many students were taking neither pineapple juice nor orange juice. ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12,13,14,15} A = multiples of 3 B = multiples of 5 (a) Complete the Venn diagram (list the numbers separated by commas - do not use brackets) A B 50 students were surveyed about the languages they study. 8 students study French and German. 30 students only study French and 3 students do not study French or German.Complete the venn diagram: F G In a survey, Sam found that 37 people liked product A,35 liked product B, and 38 liked product C. If 23 people liked both products A and B, 18 people liked products C and A, 16 people liked product B and C, and 9 liked all the three products. Find how many liked product C only? Check whether the given sets are equal sets: A = {1, 2, 3, 4} and B = {2, 4, 1, 3} Not equal Equal If C is the set of numbers which are also multiples of 3then C = {3, 6, 9, …} How would you describe set C? Finite Set Infinite Set Null Set Empty Set Are sets A and B equivalent? Yes No A group of high school students were surveyed to determine their favorite ice cream flavor. The Venn Diagram below organizes the data collected How many students like chocolate but not strawberry? How many students are in the chocolate set ? Jasper owns a bakery and is going to start making custom cakes. The set C represents several types of cakes C = {chocolate, vanilla, marble} The set F represents several types of frostings. F = (Fudge, Vanilla, Chocolate, Whipped, Fruit} How many elements are there in the union of the two sets? y is directly proportional to x. Given that y = 42 when x = 6, find the value of y when x = 80. y= Label the tables direct (d), inverse (i) or neither (n) y is inversely proportional to x. Given that y = 9 when x = 12,find the value of x when y = 4: x = y is inversely proportional to x. Given that y = 14 when x = 2, find the value of y when x = 1.5. y= How much would it cost each, if a total of 10 people came on the trip? Mark is planning a trip with his friends, he breaks down the cost per person: £ Label each graph as direct proportion, inverse proportion or neither: Use the letter d for direct, i for inverse or n for neither. a) b) c) d) How fast would you need to travel to to get to the destination in 30 mins? What is the constant of proportionality mph Teri earns a $700 bonus for selling a $3500 car. Her bonus (y) is directly proportional to the cost of the car (x)Use decimals if necessary a) Write an equation to relating y and x. b) If Teri's basic salary is $600 per week, how much will her total salary be for the week if she makes total sales of$20000 in one week? $ Write an equation relating w and t: How many gallons of water will be used in 15 minutes? Find the constant of proportionality: gallons Label the equations as direct variation, inverse variation or neither: Use the letter d, i or n 0.5y = 0.5x - 3 0.2x + y = 0 Y= 4x 4 5 = xy |