Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question 3: In a group of 400 people, 250 can speak Hindi and 200 can speak English. How many people can speak both Hindi and English? Solution 3: Let H be the set of people who speak Hindi, and E be the set of people who speak English n H E 400, n H 250, n E 200 E ? n H We know that: n H E n H n E n H E 400 250 200 n H E 400 450 n H E E 450 400 n H E 50 n H Thus, 50 people can speak both Hindi and English. Question 4: If S and T are two sets such that S has 21 elements, T has 32 elements, and elements, how many elements does S T have? Solution 4: It is given that: n S 21, n T 32, n S T **11** We know that: n S T n S n T n S T T 21 32 **11** 42 n S Thus, the set S T has 42 elements. ST has **11** Question 5: If X and Y are two sets such that X has 40 elements, X Y has 60 elements and X Y has 10 elements, how many elements does Y have? Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Solution 5: It is given that: n X 40, n X Y 60, n X Y 10 We know that: n X Y n X nY n X Y 60 40 nY 10 nY 60 40 10 30 Thus, the set Y has 30 elements. Question 6: In a group of 70 people, 37 like coffee, 52 like tea, and each person likes at least one of the two drinks. How many people like both coffee and tea? Solution 6: Let C denote the set of people who like coffee, and T denote the set of people who like tea n C T 70, n C 37, n T 52 We know that: n C T n C n T n C T 70 37 52 n C T 70 89 n C T C T 89 70 19 Thus, 19 people like both coffee and tea. Question 7: In a group of 65 people, 40 like cricket, 10 like both cricket and tennis. How many like tennis only and not cricket? How many like tennis? Solution 7: Let C denote the set of people who like cricket, and T denote the set of people who like tennis n C T 65, n C 40, n C T 10 We know that: nC T nC nT nC T Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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Class XI Chapter 12 - Introduction

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