Example 8 (ii) - Chapter 1 Class 11 Sets

Last updated at April 16, 2024 by

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

Transcript

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 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.