Class 8: Venn Diagrams Exercise 2

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1 Class 8: Venn Diagrams Exercise 2 1. Let = {a, b, c, e, f} and = {c, d, e, g} be the two subset of the universal set = {a, b, c, d, e, f, g, h}. Draw the Venn diagrams to represent these sets. From the Venn diagrams so drawn, find: i. ii. iii. iv. nswer: a b f c e d g h a b f c e d g h ( ) ( ) a b f c e d g h c d e g a b f h 1

2 2. From the djoining figure, find: vi. nswer: i. ii. iii. iv. v. ( ) ( ) i. = {, 13} Note: Take the common elements between and ii. = {, 11, 12, 13, 16, 17, 19} Note: Take all the elements from the universal set which are not in and iii. = {11, 12, 14, 1, 17, 18} Note: ll elements that are in the universal set but not in iv. = {14, 1, 16, 17, 18, 19} Note: ll elements that are in the universal set but not in v. ( ) = {14, 1, 17, 18} Note: ll elements that are in the universal set but not in ( ) vi. ( ) = {11, 12, 14, 1, 16, 17, 18, 19} Note: ll elements that are in the universal set but not in ( ) 2

3 3. Use the adjoining figure, find the following: i. ii. C iii. C iv. C v. C vi. vii. viii. C ix. C x. ( C) xi. xii. ( C) ( C) C nswers: i. = {2, 4} ii. C = {4, } iii. C = {4, 6} iv. C = {4} v. C = {2, 3, 9, 11} vi. = {2, 3, 4,, 6, } vii. = {, } viii. C = {2, 3} ix. C = {6, 7, 8} x. ( C) = {9,, 11} xi. ( C) = {3, 9, } xii. ( C) = {9, 11} 3

4 4. Use the adjacent Venn diagram to find: i. ii. iii. iv. v. vi. nswers: i. = {2, 4} ii. = {2, 4,, 7, 9} iii. = Note: There are no elements in which are not in. Hence Null set. iv. = {, 7, 9} v. = {2, 4,, 7, 9} vi. = {1, 3, 6, 8, }. Let and be sets such that n() = 17, n( )=38 and n( ) = 2. Draw Venn diagrams and find: i. n( ) ii. n() iii. n( ) nswers: i. n( ) = 13 Note: Elements which are in but not in (1-2) ii. n() = 23 Note: Total number of elements in which are (2+21) iii. n( ) = 21 Note: Elements which are in but not in (23-2) 4

5 6. In the adjoining figure, and are two sets of the universal set such that, n() = 41, n() = 2 and n() = 0. Find i. n( ) ii. n( ) iii. n( ) nswers: i. n( ) = 0 41 = 9 ii. n( ) = 0 2 = 2 iii. n( ) = 41 2 = If = {x : x N and x 20}, = {x : x is a multiple of 4}, = {x : x is a multiple of 6} and C = {x : x is a factor of 36}. Draw a Venn diagram to show that the relationship between the given sets i. C ii. iii. C nswer: The first step is to identify the elements of all the sets. They would be as below: = {1, 2, 3, 4,, 6, 7, 8, 9 18, 19, 20} = {4, 8, 12, 16, 20} = {6, 12, 18} C = {1, 2, 3, 4, 6, 9, 12, 18, 36} Now it is easy to calculate the following: i. C = {4, 12} ii. = {4, 8, 16, 20} iii. C = {12}

6 8. In a class of 60 pupils, 28 play hockey, 33 play cricket and 14 play none of these games. Draw the Venn diagram to find: i. How many play both games ii. How many play hockey only iii. How many play cricket only nswer: n() = 60 n(hockey) = 28 n(cricket) = 33 n() (n(hockey) n(cricket)) = 14 n(hockey) n(cricket) = 13 n(cricket) n(hockey) = 18 n(hockey) n(cricket) = 1 Hockey Cricket 9. In a club, three-tenths of its members play cards only and four-tenths play carom only. If 1 members play none of these games and 90 play both, find using Venn diagram, the total number of members in the club. nswer: Let the total no. of members n() = x n(cards) = 3x n(carom) = 4x n(cards) n(carom) = 90 Therefore 3x 4x = x 7x + = x 3x = Hence x = 30. Cards 3x 90 4x 1 Carom 6

7 . In a colony, two-fifths of the families read the newspaper, Times of India and threefourth of the families read Hindustan Times. If 40 families read none of these two newspaper and 0 families read both, use Venn diagram to find the number of families in the colony. nswer: Now calculate the equation: Let x be the number of families 40 ( 2x 0) ( 3x 4 0) + 40 = x 2x - 0 3x x x = Hence x = 400 Times Hindustan 11. In a class of 0 boys, 3 like horror movies, 30 like war movies, and like neither. Find the number of those who like both. nswer 1 20 Horror Movies War Movies 7

8 12. In a group of persons, each one knows either Hindi or Tamil. If 84 persons know Hindi, 36 know Tamil, and 2 know both, how many people are there in all, in the group? Tamil Hindi nswer. Total number of people in the group = In a certain locality of Delhi there are 00 families. survey showed that 04 subscribe to The Hindustan Times newspaper and 478 subscribe to The Times of India newspaper and 6 subscribe to both. Find the number of families that do not subscribe to any of these newspapers Hindustan Times Times of India nswer: Number of families which do not subscribe to any of these newspapers = 124 8

EDULABZ INTERNATIONAL SETS AND VENN DIAGRAMS

EDULABZ INTERNATIONAL SETS AND VENN DIAGRAMS 12 SETS ND VENN DIGRMS Section I : Sets 1. Describe the following sets in roster form : (i) 2 { x / x = n, n N, 2 n 5} (ii) {x / x is composite number and 11 < x < 25} (iii) {x / x W, x is divisible by