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Misc 16 - Let A = {1, 2, 3}. Then number of relations containing

Misc 16 - Chapter 1 Class 12 Relation and Functions - Part 2
Misc 16 - Chapter 1 Class 12 Relation and Functions - Part 3

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Misc 16 Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is (A) 1 (B) 2 (C) 3 (D) 4 Total possible pairs = { (1, 1) , (1, 2), (1, 3), (2, 1) , (2, 2), (2, 3), (3, 1) , (3, 2), (3, 3) } Total possible pairs = { (1, 1) , (1, 2), (1, 3), (2, 1) , (2, 2), (2, 3), (3, 1) , (3, 2), (3, 3) } Reflexive means (a, a) should be in relation . So, (1, 1) , (2, 2) , (3, 3) should be in a relation Symmetric means if (a, b) is in relation, then (b, a) should be in relation . So, since (1, 2) is in relation, (2, 1) should be in relation & since (1, 3) is in relation, (3, 1) should be in relation Transitive means if (a, b) is in relation, & (b, c) is in relation, then (a, c) is in relation We need relation which is not transitive. So, we cannot add any more pair in the relation. If we add (2, 3), we need to add (3, 2) for symmetric, but it would become transitive then Relation R1 = { So, there is only 1 possible relation Correct answer is A.

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.