Home
Class 12
MATHS
Let A={x, y, z} be a given set and a rel...

Let A={x, y, z} be a given set and a relation R on A ios defined as follows :
`R={(x,x),(y,y),(z,z),(x,y),(y,z),(z,x)}`
Then the relation R on A is -

A

symmetric only

B

transitive only

C

reflexive only

D

an equivalence relation

Text Solution

Verified by Experts

The correct Answer is:
C
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 4|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 6|80 Videos

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 2|80 Videos

  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos

  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

|{:(x,z,0),(0,y,y),(z,0,x):}|

A relation R defined on the set of natural no as follows R={(x,y),x+5y=20,x, y in N }.Find in domain and range of R.

Knowledge Check

  • 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 -

    A
    reflexive
    B
    symmetric
    C
    an equivalence relation
    D
    transitive

  • If [(x+y,2x+z),(x-y,2z+w)]=[(4,7),(0,10)] then the values of x, y, z and w are -

    A
    2, 3, 1, 2
    B
    2, 2, 3, 4
    C
    3, 3, 0, 1
    D
    2, 2, 4, 3

    • Similar Questions

    Explore conceptually related problems

    A relation R is defined on the set of integers Z Z as follows R= {(x,y) :x,y inZ Z and (x-y) is even } show that R is an equivalence relation on Z Z .

    A relation R on the set of integers Z is defined as follows : (x,y) in R rArr x in Z, |x| lt 4 and y=|x|

    Determine w hether each of the following relations are reflexive, symmetric and transitive: (i) Relation R in the set A = {1,2,3,…,13,14} defined as R = {(x,y): 3x -y =0} (ii) Relation R in the set N of natural numbers defined as R = {(x,y): y = x +5 and x lt 4} (iii) Relation R in the set A ={1,2,3,4,5,6}as R = {(x,y):y is divisible by x} (iv) Relation R in the set Z of allintegers defined as R= {(x, y) : x -y is an integer} (v) Relation R in the set A of human beings in a town at a particular time given by (a) R = {(x,y) : x and y work at the same place} (b) R = {(x,y):x and y live in the same locality] (c ) R ={(x,y) :x is exactly 7 cm taller than y} (d) R = {(x,y) :x is wife of y} (e) R = {(x,y):x is father of y}

    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.

    |{:(" "0," "x,y),(-x," "0,z),(-y,-z,0):}|=0

    Eliminate x,y and z from the following equations: (x)/(y+z)=a,y/(z+x)=b,z/(x+y)=c

    Home
    Profile