Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ BC (iii) True Let A B and B C. Let x A x B A B x C B C (iv) False Let A B 1, 2 , 0,6,8 , and Accordingly, A B and B C . However, A C (v) False Let A 3,5,7 and B 3, 4,6 C 0,1,2,6,9 Now, 5 A and A B However, 5 B (vi) True Let A B and x B. To show: x A If possible, suppose x A . Then, x B , which is a contradiction as x B xA Question 3: Let A, B and C be the set such that A B A C and A B A C Solution 3: Let, A, B and C be the sets such that A B A C and A B A C To show: B = C Let x B x A B B A B x A C A B A C x A or x C Case I Also, x B x A B x AC A B A C . Show that 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 ______________________________________________________________________________ xA xC BC and xC Similarly, we can show that C B C B. Question 4: Show that the following four conditions are equivalent: (i) A B (ii) A B (iii) A B B Solution 4: First, we have to show that Let A B To show: A B If possible, suppose A B This means that there exists A B A B A B i ii . x A, x B Let A B To show: A B Let x A Clearly, x B because if x B , then A B A B A B i ii Let A B To show: A B B Clearly, B A B Let x A B x A or x B Case I: x A x B A B A B B Case II: x B Then, AB B Conversely, let AB B Let x A , which is not possible as A B . (iv) A B A 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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