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Example 8 - Chapter 1 Class 11 Sets - Part 2

Example 8 - Chapter 1 Class 11 Sets - Part 3
Example 8 - Chapter 1 Class 11 Sets - Part 4

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Example 8 Which of the following pairs of sets are equal? Justify your answer. (ii) A = {n : n ∈ Z and n2 ≤ 4} and B = {x : x ∈ R and x2 – 3x + 2 = 0}. A = {n : n ∈ Z and n2 ≤ 4} Integers = ...... −4, −3, −2, −1, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10…. (0)2 = 0 (1)2 = 1 (2)2 = 4 (3)2 = 9 (-1)2 = 1 (-2)2 = 4 (-3)2 = 9 The elements are -2,-1,0,1,2, So, A = {–2, –1, 0, 1, 2} B = {x : x ∈ R and x2 – 3x + 2 = 0}. Solving x2 - 3x + 2 = 0, x2 – 2x – x + 2 = 0 x(x – 2) – 1(x – 2) = 0 (x – 2)(x – 1) = 0 x = 2 or x = 1 Thus, B = {1, 2}. Now, B = {1, 2} and A = {–2, –1, 0, 1, 2} Note that 0 is in set A but not in set B i.e. 0 ∈ A and 0 ∉ B, ∴ A ≠ B

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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.