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

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 (ii) (a,b) in R implies that (b,a) inR (iii) (a,b) in R and (b,c) in R implies that (a,c) in R

Let R be the relation on Z defined by R= {(a,b): a, b in Z, a-b is an integer}. Find the domain and range of R.

Let R be a relation defined by R = {(a, b) : a ge b }, where a and b are real numbers, then R is

Let R:ZrarrZ be a relation defined by R = {(a,b):a,b,inZ, a -b in z) . Show that (i) AAa inZ, (a,a) inR (ii) (a,b) inR implies (b,a)inR (iii) (a,b) inR implies (b,c)inRimplies(a,c)inR

Let R be the relation in the set N given by R={(a,b), a=b -2, b gt 6}. Choose the correct answer.

The relation R defined in A= {1,2,3} by a R b if |a^(2)-b^(2)| le 5 . Which of the following is not true?

Let R be the relation over the set N xx N and is defined by (a,b)R(c,d) implies a+d=b+c . Then R is :

Let R be the equivalence relation on z defined by R = {(a,b):2 "divides" a - b} . Write the equivalence class [0].

Let R be the relation on the set R of all real numbers defined by a R b Iff |a-b| le1. Then R is