# Example 41 - Chapter 1 Class 12 Relation and Functions

Last updated at Dec. 23, 2019 by Teachoo

Last updated at Dec. 23, 2019 by Teachoo

Transcript

Example 41, If R1 and R2 are equivalence relations in a set A, show that R1 R2 is also an equivalence relation. We have to prove R1 R2 is equivalence relation Check reflexive For all a A (a, a) R1, & (a, a) R2 Hence, (a, a) both R1 & R2 Hence, (a, a) R1 R2 R1 R2 is reflexive. Check symmetric R1 is symmetric ,hence If (a, b) R1 , then (b, a) R1 R2 is symmetric, hence If (a, b) R2 , then (b, a) R2 From (1) and (2) If (a, b) R1 R2, then (b, a) R1 R2 Hence , R1 R2 is symmetric. Checking transitive R1 is transitive, Hence, if (a, b) R1 & (b, c) R1 , then (a, c) R1 R2 is transitive, Hence, if (a, b) R2 & (b, c) R2 , then (a, c) R2 From (3) & (4) If (a, b) R1 R2 and (b, c) R1 R2 , then (a, c) R1 R2, R1 R2 is transitive. Thus, R1 R2 is an equivalence relation.

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Chapter 1 Class 12 Relation and Functions

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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.