This question is similar to Chapter 1 Class 12 Relation and Functions - Examples
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CBSE Class 12 Sample Paper for 2025 Boards
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Question 19 [Assertion Reasoning] Important
Question 20 [Assertion Reasoning] Important
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Question 36 (i) [Case Based]
Question 36 (ii)
Question 36 (iii) (A) Important
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Question 37 (i) [Case Based]
Question 37 (ii) Important You are here
Question 37 (iii) (A) Important
Question 37 (iii) (B)
Question 38 (i) [Case Based] Important
Question 38 (ii) Important
CBSE Class 12 Sample Paper for 2025 Boards
Last updated at Oct. 3, 2024 by Teachoo
This question is similar to Chapter 1 Class 12 Relation and Functions - Examples
Please check the question here
Question 37 (ii) Write the smallest equivalence relation on 𝐆. Given G = {g1, g2} We need to find smallest equivalence relation on 𝐆. Total possible pairs = {(g1, g1) , (g1, g2), (g2, g1), (g2, g2)} Reflexive means (a, a) should be in relation . So, (g1, g1) , (g2, g2) should be in a relation. It’s important that both are elements of the relation Symmetric means if (a, b) is in relation, then (b, a) should be in relation . So, since (g1, g2) is in relation, (g2, g1) should also be in relation But this also is possible if we only have (g1, g1) and (g2, g2) in the relation Transitive means if (a, b) is in relation, & (b, c) is in relation, then (a, c) is in relation So, if (g1, g2) is in relation, & (g2, g1) is in relation, then (g1, g1) should be in relation But this also is possible if we only have (g1, g1) and (g2, g2) in the relation Thus, Smallest equivalence relation on G = {(g1, g1), (g2, g2)}