Home
Class 12
MATHS
Let f : X->Ybe a function. Define a rel...

Let `f : X->Y`be a function. Define a relation R in X given by `R = {(a , b): f(a) = f(b)}`. Examine if R is an equivalence relation.

Text Solution

Verified by Experts

The correct Answer is:
`(a, c)inR`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise CHECK YOUR UNDERSTANDING|10 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise COMPETITION FILE (Questions from JEE Main)|7 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise Exercise|10 Videos
  • PROBABILITY

    MODERN PUBLICATION|Exercise MOCK TEST SECTION D|6 Videos
  • THREE DIMENSIONAL GEOMETRY

    MODERN PUBLICATION|Exercise CHAPTER TEST 11|11 Videos

Similar Questions

Explore conceptually related problems

Let quad f:X rarr Y be a function.Define a relation R in X given by R={(a,b):f(a)=f(b)} Examine if R is an equivalence relation.

Let f:X rarr Y be a function.Define a relation R in X given by R={(a,b):f(a)=f(b)} Examine whether R is an equivalence relation or not.

Knowledge Check

  • The function f :R to R defined by f (x) = e ^(x) isd

    A
    Onto
    B
    Many-one
    C
    One-one and into
    D
    Many one and onto
  • The function f: R to R defined by f(x) = 4x + 7 is

    A
    one-one
    B
    onto
    C
    into
    D
    bijective
  • Let f : R to R be any function. Define g : R to R by g(x) =|f(x)| for all x. Then g is

    A
    onto if f is onto
    B
    one-one if f is one-one
    C
    continuous if f is continuous
    D
    differentiable if f is differentiable
  • Similar Questions

    Explore conceptually related problems

    Let f:X rarr Y be a function.Define a relation R in X given by R={(a,b):f(a)=f(b)} Examine whether R is an equivalence relation or not.

    Let R be a relation on the set Q of all rationals defined by R={(a,b):a,binQ" and "a-binZ}. Show that R is an equivalence relation.

    Let R be the relation on set A={x:x in Z, 0 le x le 10} given by R={(a,b):(a-b) "is divisible by " 4} . Show that R is an equivalence relation. Also, write all elements related to 4.

    The function f : R to R defined by f (x) = |x| is :

    Let f: R to R be any function. Define g : R to R by g(x) = | f(x), AA x . Then, g is