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Number of elements
Last updated at May 29, 2023 by Teachoo
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)