Home
Class 12
MATHS
Prove that on the set of integers, Z, th...

Prove that on the set of integers, Z, the relation R defined as `aRbiffa=pmb` is an equivalence relation.

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (a) (Long Answer Type Questions (I))|7 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (a) (Long Answer Type Questions (II))|6 Videos

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise QUESTIONS FROM NCERT EXEMPLAR|5 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

In the set Z of all integers, which of the following relation R is not an equivalence relation?

The relation R on R defined as R={(a ,b) : a <=b } is an equivalence relation. State true or false.

Let Z be the set of integers.Show that the relation R={(a,b):a,b in Z and a+b is even } is an equivalence relation on Z .

Let Z be the set of integers.Show that the relation R={(a,b):a,b in Z and a+b is even } is an equivalence relation on Z .

Show that the relation R on the set Z of integers,given by R={(a,b):2 divides a-b}, is an equivalence relation.

If l is the set of integers and if the relation R is defined over l by aRb, iff a - b is an even integer, a,b inl , the relation R is

If I be the set of integers and if the relation R be defined over I by a R iff a-b is an integer,a,b in I, Then Relation R is

Show that the relation R in the set Z of integers, given by R = {(a, b): 3 divides a − b} is an equivalence relation. Hence find the equivalence classes of 0, 1 and 2.

Prove that the relation R on Z defined by (a,b)in R hArr a-b is divisible by 5 is an equivalence relation on Z .

Let M be the set of men and R is a relation is son of defined on M.Then,R is ( a) an equivalence relation (b) a symmetric relation (c) a transitive relation (d) None of these