Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ Question 8: Show that for any sets A and B, A A B A B Solution 8: To show: Let x A and A A B A B We have to show that Case I x A B Then, Case II xAB A B A A B x A B A B x A B A B A B x A or x B x B x A x A B A B A B ....... 1 A A B A B It is clear that A B A A B A and A B A B A ....... 2 From (1) and (2), we obtain A A B A B To prove: Let x A B A xA A B A A B or x B and x A x A or x Band x A or x A x A B A B A A B ..... 3 Next, we show that A B A B A . Let y A B y A or y B y A or y Band y Aor y A Printed from Vedantu.com. Register now to book a Free LIVE Online trial session with a Top tutor.

Class XI Chapter 1 – Sets Maths ______________________________________________________________________________ y A or y B and y A y A B A A B A B A ..... 4 Hence, from (3) and (4), we obtain A B A A B . Question 9: Using properties of sets show that (i) (ii) A A B A Solution 9: (i) To show: We know that A A A B A A A B A A A B A..... 1 Also, A A A B ...... 2 A A B A From1 and 2 , A A B A (ii) To show: A A B A A A B A A A B A A B A from 1 Question 10: Show that A B A C need not imply B = C. Solution 10: Let A0,1 , B 0, 2,3 , and C 0,4,5 Accordingly, Here, A B A C A B 0 and A C 0 0 However, B C 2 B and 2 C 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 4 - Principle of M

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Class XI Chapter 8 - Binomial Theor

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Class XI Chapter 12 - Introduction

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Class XI Chapter 13 - Limits and De

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Class XI Chapter 15 - Statistics Ma

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