Home
Class 11
MATHS
Let R be a relation from N to N defined ...

Let R be a relation from N to N defined by `R={(a,b): a, b in N and a=b^(2)).` Are the following true?
(i) `(a,a) in R," for all " a in N` (ii) `(a,b) in R," implies "(b,a) in R`
(iii) `(a,b) in R, (b,c) in R" implies "(a,c) in R`.
Justify your answer in each case.

Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT TELUGU|Exercise Exercise 2.3|5 Videos

  • PROBABILITY

    NCERT TELUGU|Exercise MISCELLANEOUS EXERCISEON CHAPTER 25|1 Videos

  • SEQUENCES AND SERIES

    NCERT TELUGU|Exercise Miscellaneous Exercise On Chapter 9|31 Videos

Similar Questions

Explore conceptually related problems

Let R be a relation from Q to Q defined by R={(a,b): a,b in Q and a-b in Z} . Show that (i) (a,a) in R" for all " a in Q

Show that * : R xx R to R defined by: a * b =a-5b is not abelian.

N is the set of natural numbers and R is a relation on N xx N defined by (a, b)R(c, d) if an only if a+d=b+c then R is

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.

If a relation R is defined on the set Z of integers as follows (a,b)in R iff a^(2)+b^(2)=25 then, domain ( R ) =

Let f: X to 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.