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Ex 1.1, 7 - Relation R in set A of all books in a library - Ex 1.1

Ex 1.1, 7 - Chapter 1 Class 12 Relation and Functions - Part 2
Ex 1.1, 7 - Chapter 1 Class 12 Relation and Functions - Part 3

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Ex 1.1, 7 Show that the relation R in the set A of all the books in a library of a college, given by R = {(x, y): x and y have same number of pages} is an equivalence relation. R = {( x, y): x and y have same number of pages} Check reflexive If reflexive , then (x, x) R Book x and Book x have the same number of pages. Which is always true. Hence, R is reflexive Check symmetric If x and y have the same number of pages, then we can say that y and x have the same number of pages. Hence If (x, y) R, then (y, x) R R is symmetric. Check transitive If x and y have the same number of pages. & y and z have the same number of pages. then, x and z have the same number of pages. Hence , If (x, y) R & (y, z) R , then (x, z) R R is transitive Since R is reflexive, symmetric and transitive Hence, R is an equivalence relation.

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Davneet Singh

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.