Ex 1.1, 10 (v) - Chapter 1 Class 12 Relation and Functions
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Ex 1.1, 10
Given an example of a relation. Which is
(v) Symmetric and transitive but not reflexive.
Let A = {1, 2, 3}.
Let relation R on set A be
Let R = {(1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)}
Check Reflexive
If the relation is reflexive,
then (a, a) R for every a {1,2,3}
Since (1, 1), (2, 2), (3, 3) R
R is not reflexive
Check Symmetric
Since (1, 2) R , (2, 1) R
& (1, 3) R , (3, 1) R
& (2, 3) R , (3, 2) R
So, If (a, b) R, then (b, a) R
R is symmetric.
Check transitive
Since (1, 2) R , (2, 3) R & (1, 3) R
& (2, 1) R , (1, 3) R & (2, 3) R
& (3, 1) R , (1, 2) R & (3, 2) R
So, If (a, b) R , (b, c) R , then (a, c) R
R is transitive.
Hence, relation R is symmetric and transitive but not reflexive
Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.
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