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

Show that the relation R in the set `A = {1,2,3,4,5}` given by
`R = {(a,b) : |a-b|` is even}, is an equivalence relation. Show that all the elements of `{1,3,5}` are related to each other and all the elements of `{2,4}` are related to each other. But no element of `{1,3,5}` is related to any element of `{2,4}.`

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.2|11 Videos

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise EXERCISE 1.3|14 Videos

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise MISCLELLANEOUS EXERCISE ON CHAPTER 1|18 Videos

  • PROBABILITY

    NCERT TELUGU|Exercise MISCELLANEOUS EXERCISE ON CHAPTER 13|19 Videos

  • VECTOR ALGEBRA

    NCERT TELUGU|Exercise Miscellaneous Exercise on chapter 10|17 Videos

Similar Questions

Explore conceptually related problems

Let R be the realtion defined in the set A = {1,2,3,4,5,6,7} by R ={(a,b): both a and b are either odd or even}. Show that R is an related to each other and all the elements of the subset {2,4,6} are related to each other, but no element of the subset {1,3,5,7} is related to any element of the subset {2,4,6}.

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

Show that the relation R in the set {1,2,3} given by R = {(1,1) ,(2,2),(3,3) , (1,2) ., (2,3)} is reflexive but neither symmetric nor transitive.

Show that the relation R in the set R of real numbers, defined as R = {(a,b) : a le b ^(2)} is neither reflexive nor symmetric nor transitive.

The relation R={(1,1),(2,2),(3,3)} on the set {1, 2, 3) is