Home
Class 12
MATHS
Let n be a fixed positive integer. Defin...

Let n be a fixed positive integer. Define a relation R on Z as follows for all a, b `in` Z, aRb, if and only if a-bis divisible by n. Show that R is an equivalence relation.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE ( Long Answer Type Questions ) |14 Videos

  • RELATIONS AND FUNCTIONS

    ARIHANT PUBLICATION|Exercise CHAPTER PRACTICE (Very Short Answer Type Questions ) |19 Videos

  • QUESTION PAPER 2020

    ARIHANT PUBLICATION|Exercise GROUP C (ANSWER ANY ONE QUESTIONS)|13 Videos

  • SAMPLE PAPER 1

    ARIHANT PUBLICATION|Exercise LONG ANSWER TYPE QUESTIONS|13 Videos

Similar Questions

Explore conceptually related problems

Let R={(m,n):2 divides m+n} on Z. Show that R is an equivalence relation on Z.

If Z is the set of all integers and R is the relation on Z defined as R={(a, b): a, b in Z and a-b is divisible by 3. Prove that R is an equivalence relation.

Let R be the relation on Z defined by aRb iff a-b is an even integer. Show that R is an equivalence relation.

Prove that the relation R on the set Z of all integers defined by R={(a, b):a-b is divisible by n} is an equivalence relation.

Let R be a relation on the set A of ordered pairs of positive integers defined by (x, y) R (u, v), if and only if xv = yu. Show that R is an equivalence relation.

The ralation R on Z is defined by for m, nin Z , mRnimpliesm/n is a power of 2. Examine whether it is an equivalence relation.

Show that if R is an equivalence relation on X then dom R=rngR =X.

If N denotes the set of all natural numbers and R be the relation on N xx N defined by (a, b) R (c, d) if ad(b+ c)=bc(a+d) . Show that R is an equivalence relation.

If f:X to Y is a function. Define a relation R on X given by R={(a, b): f(a)=f(b)}. Show that R is an equivalence relation on X.

Let R be a relation in the set of natural numbers N defined by xRy if and only if x+y=18 . Is R an equivalence relation?