Home
Class 12
MATHS
Let RR be a relation defined on the ...

Let `RR ` be a relation defined on the set `ZZ` of all integers and `xRy ` when ` x+2y ` is divisible by 3, then

A

R is not transitive

B

R is symmetric only

C

R is an equivalence relation

D

R is not an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE main (AIEEE ) Archive|3 Videos
  • RELATION AND FUNCTIONS

    CHHAYA PUBLICATION|Exercise JEE Advanced Archive|3 Videos
  • RELATION AND MAPPING

    CHHAYA PUBLICATION|Exercise Assertion Type|2 Videos
  • RELATIONS

    CHHAYA PUBLICATION|Exercise Sample Question for Competitive Examination (Assertion -Reason Type )|2 Videos

Similar Questions

Explore conceptually related problems

The relation R defined on the set N N of natural numbers by xRy iff 2x^(2) -3xy +y^(2) =0 is

A relation R is defined on the set of all integers Z Z follows : (x,y) in "R" implies (x,y) is divisible by n Prove that R is an equivalence relation on Z Z .

A relation R is defined on the set of all natural numbers NN by : (x,y) in Rimplies (x-y) is divisible by 6 for all x,y,in NN prove that R is an equivalence relation on NN .

A realation rho is defined on set Z , a set of all integers , such that rho ={(x,y) in Z xx Z :Y -x is divisible by 5} . Discuss whether rho is an equialence relation . IF A ={x in Z: (2 ,x) in rho , -10 le x le 10} then mention the elements of A .

A relation R is defined on the set of natural numbers NN as follows : (x,y)in R rArr y is divisible by x, for all x, y in NN . Show that, R is reflexive and transitive but not symmetric on NN .

A relation R is defined on the set of all natural numbers IN by: (x,y)inRimplies(x-y) is divisible by 5 for all x,y inIN . Prove that R is an equivalence relation on IN.

If ** be the binary operation on the set ZZ of all integers, defined by a**b=a+3b^(2) , find 2**4.

A binary operation ** is defined on the set ZZ of all integers by a@b=a+b-3 for all a,binZZ . Determine the inverse of 5inZZ .

A relation R is defined on the set of integers Z as follows: R{(x,y):x,y in Z and x-y" is odd"} Then the relation R on Z is -

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.