CBSE Class 12 Sample Paper for 2021 Boards
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CBSE Class 12 Sample Paper for 2021 Boards
Last updated at Dec. 16, 2024 by Teachoo
Transcript
Question 3 (Choice 2) An equivalence relation R in A divides it into equivalence classes 𝐴1, 𝐴2, 𝐴3. What is the value of 𝐴1 ∪ 𝐴2 ∪ 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 ∪ 𝐴2 ∪ 𝐴3 = {1, 2, 3} And 𝐴1 ∩ 𝐴2 ∩ 𝐴3 = 𝜙 Similarly, for any equivalence class 𝐴1, 𝐴2, 𝐴3 𝐴1 ∪ 𝐴2 ∪ 𝐴3 = A And 𝐴1 ∩ 𝐴2 ∩ 𝐴3 = 𝝓
