Question

What is Relation define it and explain domain and range of the relation. Let A= {1,2,3,
.,14) and R be a relation from A to A such that R = {(x,y): 3x - y = 0, where x,y E Z}.Write
its domain , codomain and range.
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Answer 1

Relation:- A relation R from a non empty set A to a non empty set B is a subset of the cartesian product A×B.

Domain:-Domain is a set of all first elements of the ordered pair in a relation.

Range:-Range is the set of all second elements of the ordered pair in a relation

R={(x,y):3x-y=0,where x,y E A}={(1,3),(2,6),(3,9),(4,12)}

please see the above image .....

Domain={1,2,3,4}

Co-domain={1,2,3,4........14}

Range={3,6,9,12}

Answer 2

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It is given that the relation R from A to A is given by R = {(x, y): 3x – y = 0, where x, y ∈ A}.

It means that R = {(x, y) : 3x = y, where x, y ∈ A}

Hence, R = {(1, 3), (2, 6), (3, 9), (4, 12)}

We know that the domain of R is defined as the set of all first elements of the ordered pairs in the given relation.

Hence, the domain of R = {1, 2, 3, 4}

To determine the codomain, we know that the entire set A is the codomain of the relation R.

Therefore, the codomain of R = A = {1, 2, 3,…,14}

As it is known that, the range of R is defined as the set of all second elements in the relation ordered pair.

Hence, the Range of R is given by = {3, 6, 9, 12}

Hope it's Helpful.....:)