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

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

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

  1. Chapter 1 Class 12 Relation and Functions (Term 1)
  2. Serial order wise

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
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.