SETS

1. The diagram is a Venn diagram which shows the universal set ξ, sets S and T. Which of the following sets has region that is equivalent to the region (S ∩ T)'? S ' ∪ T ' S ' ∪ T S ' ∩ T S ∪ T ' 2.It is given that the universal set, ξ = X ∪ Y ∪ Z, X ⊂ Y and Y ∩ Z = ∅.Which Venn diagram represents these relationship? 3.It is given that universal set ξ = {x: 1 ≤ x ≤ 20, x is an integer}, set X = {x: x is a multiple of 2} and set Y = {x: x is a multiple of 4}.Which statement is true? (X ∩ Y) = X Y ⊄ X (X ∩ Y) = Y X ⊂ Y 4. Choose the correct Venn diagram represents set S ⊂ T such that the universal set ξ = S ∪ T. 5. Given that the universal set ξ = P ∪ Q, set P = {g, h, i, j, k, l} and set Q = {w, x, y}. Find the value of n(ξ). 12 11 10 9 6. The diagram is a Venn diagram which shows the universal set ξ, sets X and Y.Determine the set which represents the shaded region in the Venn diagram. X ' ∩ Y ' X ∪ Y ' X ∪ Y X ∩ Y ' 7. Which of the Venn diagrams represents the set M ∪ N = M such that the universal set ξ = M ∪ N? 8. The diagram is a Venn diagram showing the number of competition participants in set P and set Q. Given that the universal set, ξ = P ∪ Q, set P = {singing competition participants} and set Q = {drawing competition participants}.If the number of participants who participate in only one competition is 34, find the total number of the participants. 38 40 42 45 9. The diagram is a Venn diagram showing the number of elements in set X, set Y and set Z.It is given that the universal set, ξ = X ∪ Y ∪ Z and n(ξ) = 24.Find the value of n(Z'). 20 18 11 9 10. The diagram shows a Venn diagram with the universal set ξ = X ∪ Y ∪ Z.Which of the region A, B, C or D represents the set X ' ∩ Y ∩ Z '? A B C D 11. The Venn diagram shows the elements of the universal set ξ, set M and set N.List all the elements of set N '. {c, i, j} {c, d, f, j, k, l} {c, d, f, i, j, k, l} {b, c, d, e, f, g, i, j, k, l} 12. The diagram shows a Venn diagram with the universal set ξ = {Form 4 students}, set X = {Students who like to play badminton} and set Y = {Students who like to play basketball}.Given that n(ξ) = 170, n(X) = 52, n(Y) = 38 and n(X ∩ Y) = 26. Find the number of students who do not like to play both the badminton and basketball. 132 106 80 64 13. Given that the universal set ξ = {x : 17 < x ≤ 33, x is an integer} and set X = {x : x is a number which the sum of its two digits is an even number}. Find X '. {18, 19, 21, 23, 25, 29, 30, 32} {18, 21, 22, 23, 25, 27, 29, 30, 32} {18, 21, 23, 25, 27, 29, 30, 32} {19, 20, 22, 24, 26, 28, 31, 33} 14. The Venn diagram shows the universal set ξ, sets X and Y.Determine the set which represents the shaded region in the Venn diagram. X ∩ Y X ∪ Y X' ∪ Y ' X ' ∩ Y ' 15.Given that the universal set, ξ = P ∪ Q, set P = {1, 2} and set Q = {0, 1, 2}.Find the value of n(ξ). 2 3 5 6 16. Diagram 15 is a Venn diagram which shows the elements of sets X, Y and Z.If the universal set ξ = X ∪ Y ∪ Z, what is the elements of set X ∩ Y '? {4} {2, 3, 4} {2, 3, 4, 5, 7, 8} {1, 2, 3, 4} 17. The table shows the result of a survey of 95 magazine readers.MagazineNumber of readersFashion48Entertainment48Fashion and Entertainment only20Fashion and Sports only11Fashion only10Entertainment only12The Venn diagram represents part of the information.Find the number of magazine readers who like to read fashion magazine or sports magazine and also entertainment magazine. 59 48 47 36 18. The diagram is a Venn diagram which shows the elements of sets X, Y and Z.Given that the universal set ξ = X ∪ Y ∪ Z and n(Z ') = n(Y ∩ Z). Determine the value of x. 1 2 6 9 19. The diagram shows a Venn diagram with the universal set ξ = {Students in class 5A}, set X = {Students who are passed the Mathematics test} and set Y = {Students who are passed the Science test}.Given that n(X) = 19, n(Y) = 9, n(X ∩ Y ') = 12, and the number of students who failed both of the tests is 14 persons. Calculate the total number of students in class 5A. 28 35 42 54 20. The diagram shows a Venn diagram with the number of students in sets X, Y and Z. It is given that set X = {Students who registered Mathematic tuition class}, set Y = {Students who registered Science tuition class}, set Z = {Students who registered English tuition class} and the universal set ξ = X ∪ Y ∪ Z.If the number of students who registered Mathematic tuition class and Science tuition class is 23, find the number of students who registered only one tuition class. 46 37 35 27 21. Given that Q = {factors of 8}, find n(Q). 5 6 7 8 22. Given X = {colours of the Malaysian flag). Which of the following is false? white is an element of X red is an element of X blue is an element of X green is an element of X 23. Given that the universal set ξ = {x : 5 ≤ x ≤ 21, x is an integer}, set A = {6, 8, 11, 16}, set B = {x : x is an odd number} and set C = {x : x is a multiple of 5}. State the elements in the set (A ∪ B)' ∩ C. 6, 8, 10, 12, 14, 16, 18, 20 5, 10, 15, 20 10, 20 5, 15 Match acordingly. Intersection of sets The common elements of all the sets. Complement of set All the elements not in the sets Union of sets All the elements in the sets Complement of union of sets All the elements not in the union of sets