Home
Class 12
MATHS
Let A = {1, 2, 3} and R = {(a,b): a,b in...

Let A = {1, 2, 3} and R = {(a,b): `a,b in A, a` divides b and b divides a}. Show that R is an identity relation on A.

Text Solution

Verified by Experts

Given, A = {1, 2, 3}
`a in A, b in B`, a divides b and b divides a.
implies a = b
`therefore R={(a,a),ainA}={(1,1),(2,2),(3,3)}`
Hence, R is the identity relation on A.
Promotional Banner

Similar Questions

Explore conceptually related problems

Let A = {3,5}, B = {7,1}. Let R = {(a,b): ainA, binB, a-b is even}. Show that R is an universal relation from A to B.

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}.

Let n be a fixed positive integer. Define a relation R on Z as follows: (a ,\ b) in RhArra-b is divisible by ndot Show that R is an equivalence relation on Zdot

Let A = ( a, b, c) and R = {(a, a), (b, b), (a, b), (b, a), (b, c)} be a relation on A, then R is

Let A={x in Z:0 le x le 12} . Show that R={(a,b):a,b in A,|a-b|is divisible by 4} is an equivalence relation. Find the set of all elements related to 1. Also write the equivalence class [2]

Let A = { 2, 3, 4} and R be relation on A defined by R={(x,y)(x,yinA,x divides y } , find 'R'.

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 A = {1, 2, 3} and B={2, 3, 4} , then which of the following relation from A to B is a function from A into B