Home
Class 11
MATHS
Let R be the relation on Z defined by 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.

Text Solution

AI Generated Solution

To solve the problem, we need to analyze the relation \( R \) defined on the set of integers \( \mathbb{Z} \) such that \( R = \{(a, b) : a, b \in \mathbb{Z}, ab \text{ is an integer}\} \). ### Step 1: Understanding the Relation The relation \( R \) consists of pairs \( (a, b) \) where both \( a \) and \( b \) are integers, and their product \( ab \) is also an integer. Since the product of any two integers is always an integer, this condition is satisfied for all integers \( a \) and \( b \). ### Step 2: Finding the Domain The domain of a relation is the set of all first elements in the ordered pairs. In this case, since \( a \) can be any integer, the domain of \( R \) is the set of all integers. ...
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise SOLVED EXAMPLES|22 Videos

  • RELATIONS AND FUNCTIONS

    NCERT ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • PROBABILITY

    NCERT ENGLISH|Exercise All Questions|71 Videos

  • SEQUENCES AND SERIES

    NCERT ENGLISH|Exercise EXERCISE 9.5|6 Videos

Similar Questions

Explore conceptually related problems

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

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

Let A = {1, 2, 3, 4, 6} . Let R be the relation on A defined by {(a , b): a , b in A , a is exactly divisible by b}.(i) Write R in roster form(ii) Find the domain of R(iii) Find the range of R.

Let A={1,2,3,4,6} . Let R be the relation on A defined by {(a,b)=ainA,binA," a divides b"} . Find (i) R (ii) domain of R (iii) 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 A={2,3,4,5,6,7,8,9} Let R be the relation on A defined by {(x,y):x epsilonA,yepsilonA & x^(2)=y or x=y^(2) }. Find domain and range of R .

Let A = {1, 2, 3, 4, 6} . Let R be the relation on A defined by {(adot b): a , b in A , b is exactly divisible by a}.(i) Write R in roster form(ii) Find the domain of R(iii) Find the range of R.

Let Z be the set of all integers and R be the relation on Z defined as R={(a , b); a ,\ b\ in Z , and (a-b) is divisible by 5.} . Prove that R is an equivalence relation.

Let Z be the set of all integers and R be the relation on Z defined by R= { (a,b): a, b in Z and (a-b) is divisible by 5} . Prove that R is an equivalence relation

Let A={1,2,3,4,5,6}dot Let R be a relation on A defined by R={(a , b): a , b in A , b is exactly divisible by a } Write R is roster form Find the domain of R Find the range of Rdot