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An equivalence relation R in A divides it into equivalence classes 𝐴1,𝐴2, 𝐴3. What is the value of 𝐴1 βˆͺ 𝐴2 βˆͺ 𝐴3 and 𝐴1 ∩ 𝐴2 ∩ 𝐴3

An equivalence relation R in A divides it into equivalence classes A1

Question 3  (Choice 2) - CBSE Class 12 Sample Paper for 2021 Boards - Part 2

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Question 3 (Choice 2) An equivalence relation R in A divides it into equivalence classes 𝐴1, 𝐴2, 𝐴3. What is the value of 𝐴1 βˆͺ 𝐴2 βˆͺ 𝐴3 and 𝐴1 ∩ 𝐴2 ∩ 𝐴3 Let R = {(1, 1), (2, 2), (3, 3)} be an equivalence relation A1 is the equivalence class containing one element as 1 ∴ A1 = {1} A2 is the equivalence class containing one element as 2 ∴ A2 = {2} A3 is the equivalence class containing one element as 3 ∴ A3 = {3} Now, 𝐴1 βˆͺ 𝐴2 βˆͺ 𝐴3 = {1, 2, 3} And 𝐴1 ∩ 𝐴2 ∩ 𝐴3 = πœ™ Similarly, for any equivalence class 𝐴1, 𝐴2, 𝐴3 𝐴1 βˆͺ 𝐴2 βˆͺ 𝐴3 = A And 𝐴1 ∩ 𝐴2 ∩ 𝐴3 = 𝝓

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