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Ex 2.1, 10 - The Cartesian product A x A has 9 elements - Ex 2.1

Ex 2.1, 10 - Chapter 2 Class 11 Relations and Functions - Part 2
Ex 2.1, 10 - Chapter 2 Class 11 Relations and Functions - Part 3

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Ex 2.1, 10 The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A. Since A × A has 9 elements So, A would have 3 elements Let A = {a, b, c} Now, A × A = {a, b, c} × {a, b, c} = { (a, a) , (a, b) , (a, c), (b, a) , (b, b) , (b, c), (c, a) , (c, b) , (c, c)} (As 3 × 3 = 9) Now, (–1,0) is in set A × A And, (0, 1) is in set A × A Thus, a = –1 , b = 0, c = 1 So, A = { a, b, c} = {– 1, 0, 1}. Now A × A = {– 1, 0, 1} × {– 1, 0, 1} A × A = {(–1, –1), (– 1, 1), (–1, 0) (0, – 1), (0, 0), (0, 1), (1, – 1), (1, 0),(1, 1)} (Taking a = –1, b = 0) (Taking b = 0, c = 1) Thus, remaining elements of set A × A are (– 1, – 1), (– 1, 1), (0, – 1), (0, 0), (1, – 1), (1, 0), and (1, 1)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.