An equivalence relation R in A divides it into equivalence classes ๐ด1,๐ด2, ๐ด3. What is the value of ๐ด1 ∪ ๐ด2 ∪ ๐ด3 and ๐ด1 ∩ ๐ด2 ∩ ๐ด3

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  1. Class 12
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Transcript

Question 3 (Choice 2) An equivalence relation R in A divides it into equivalence classes ๐ด1, ๐ด2, ๐ด3. What is the value of ๐ด1 โˆช ๐ด2 โˆช ๐ด3 and ๐ด1 โˆฉ ๐ด2 โˆฉ ๐ด3 Let R = {(1, 1), (2, 2), (3, 3)} be an equivalence relation A1 is the equivalence class containing elements as 1 โˆด A1 = {1} A2 is the equivalence class containing elements as 2 โˆด A2 = {2} A3 is the equivalence class containing elements as 3 โˆด A3 = {3} Now, ๐ด1 โˆช ๐ด2 โˆช ๐ด3 = {1, 2, 3} And ๐ด1 โˆฉ ๐ด2 โˆฉ ๐ด3 = ๐œ™ Similarly, for any equivalence class ๐ด1, ๐ด2, ๐ด3 ๐ด1 โˆช ๐ด2 โˆช ๐ด3 = A And ๐ด1 โˆฉ ๐ด2 โˆฉ ๐ด3 = ๐“

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.