Check sibling questions

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Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


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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 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.