Home
Class 12
MATHS
Show that the relation R in the set A={x...

Show that the relation R in the set `A={x in z, 0 le x le 12}` given by `R={(a,b):|a-b|` is a multiple of 4} is an equivalence relation.

Text Solution

Verified by Experts

The correct Answer is:
`{2, 6, 10}`
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (b) (Long Answer Type Questions (I))|15 Videos
  • RELATIONS AND FUNCTIONS

    MODERN PUBLICATION|Exercise EXERCISE 1 (c) (Short Answer Type Questions)|7 Videos
  • RELATIONS AND FUNCTIONS

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

Show that the relation R on the set A={x in Z:0<=x<=12}, given by R={(a,b):|a-b| is a multiple of 4} is an equivalence relation.Find the set of all elements related to 1 i.e.equivalence class [1]

Show that the relation R in the set A={x in N:0<=x<=12 } given by R={ (a,b):|a-b| is a multiple of 4 } is an equivalence relation?

Let the relation R in the set A = {x in z: 0 le x le 12} given by R= {(a, b) :la - bl is a multiple of 4}. Then [1], the equivalence class containing 1, is:

Show that the relation S on the set : A={x inZ:0lexle12} given by: S = { (a,b):a,binZ,|a-b| is divisible by 3} is an equivalence relation.

Let the relation R in the set A = {x in Z : 0 le x le 12} , given by R = {(a, b) : |a – b|" is a multiple of "4} . Then [1], the equivalence class containing 1, is:

Show that the relation R in the set A={x: x in N,x <=10} given by R={(a, b):a+ b is even number] is an equivalence relation. Also find the set of all elements related to 3

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.

Show that the relation R in the set A = {1, 2, 3, 4, 5,6,7} given by R = {(a , b) : |a - b| " is even" } , is an equivalence relation.

Show that the relation R in the set A={1,2,3,4,5} given by R={(a,b):|a b | is divisible by 2} is an equivalence relation.Write all the quivalence classes of R .

Show that the relation S in the set A={x in Z:0<=x<=12} given by S={(a,b):a,b epsilon Z,^(-)|a-b| is divisible by 4} is an equivalence relation.Find the set of all elements related to 1.