Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question **11**: Let A and B be sets. If A X B X B. (Hints , A A A X B B B X Solution **11**: Let A and B be two sets such that To show: A = B It can be seen that and A X B X A A A X A B X A X B X A B A X A B A X A B..... 1 Now, B B B X B A X A X B X B A B X B A B X B A A B..... 2 Hence, from (1) and (2), we obtain A = B. and use distributive law) A X B x f and A X B X [Distributive law] [Distributive law] for some set X, show that A = for some set X. Question 12: Find sets A, B and C such that A B, B C and A C Solution 12: Let A 0,1 , B 1,2 , and C 2,0 . Accordingly, A B B C A C 1 , 2 ,and 0 . A B, B C, and A C are non-empty. However, A B C are non-empty sets and A B C Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question 13: In a survey of 600 students in a school, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee? Solution 13: Let U be the set of all students who took part in the survey. Let T be the set of students taking tea. Let C be the set of students taking coffee. Accordingly, nU 600, nT 150, nC 225, nT C 100 To find: Number of student taking neither tea nor coffee i.e., we have to find n T ' C ' n T C ' n U n T C n U n T n C n T C 600 150 225 100 600 275 = 325 Hence, 325 students were taking neither tea nor coffee. n T ' C ' . Question 14: In a group of students 100 students know Hindi, 50 know English and 25 know both. Each of the students knows either Hindi or English. How many students are there in the group? Solution 14: Let U be the set of all students in the group. Let E be the set of all students who know English. Let H be the set of all students who know Hindi. H E U Accordingly, nH 100 and n E 50 nH E 25 nU nH nE nH E 100 50 25 125 Hence, there are 125 students in the group. Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

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