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Ex 1.1, 1 - Chapter 1 Class 12 Relation and Functions - Part 9

Ex 1.1, 1 - Chapter 1 Class 12 Relation and Functions - Part 10
Ex 1.1, 1 - Chapter 1 Class 12 Relation and Functions - Part 11

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Transcript

Ex 1.1, 1 Determine whether each of the following relations are reflexive, symmetric and transitive: (iv) Relation R in the set Z of all integers defined as R = {(x, y): x y is as integer} R = {(x, y): x y is as integer} Check Reflexive Since, x x = 0 & 0 is an integer x x is an integer (x, x) R R is reflexive Check symmetric If x y is an integer, then (x y) is also an integer, y x is an integer So, If x y is an integer, then y x is an integer i.e. If (x, y) R, then (y, x) R R is symmetric Check transitive If x y is an integer & y z is an integer then, sum of integers is also an integer (x y) + (y z) is an integer. x z is an integer. So, If x y is an integer & y z is an integer then, x z is an integer. If (x, y) R & (y, z) R , then (x, z) R R is transitive Hence, R is reflexive, symmetric, and transitive.

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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.