Question

What is the domain of the relation {(3, 4), (1, 3), (1, 4), (5, 2)}?

Answer 1

Answer:

Step-by-step explanation:

Let A = {1, 2, 3, 4,..., 45} and R be the relation defined as “is square of ” on A. Write R as a subset of A x A. Also, find the domain and range of R.

Solution :

A = {1, 2, 3, 4,..., 45}

Let "A" be a set which contains some of elements of A

A = {1, 2, 3, 4, 5, 6}

Now, we have to write the other set of elements from A. The elements in this set denotes the square value of previous set.

Square values of set A  =  {1, 4, 9, 16, 25, 36}

A x A  =  {(1, 1)(1,4)(1, 9)(1, 16) (1, 25)  (1, 36)..................}

Domain  =  {1, 2, 3, 4, 5, 6}

Range  =  {1, 4, 9, 16, 25, 36}

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Answer 2

SOLUTION

TO DETERMINE

The domain of the relation {(3, 4), (1, 3), (1, 4), (5, 2)}

EVALUATION

First we learn what is relation

Let A and B are two sets. Then the Cartesian product of A and B is denoted by A × B and defined as

$\sf{A \times B = \{(x, y) : x \in A \: \: and \: \: y \in B \}}$

Now a Relation R from A to B is a Subset of A × B

Here the given relation is {(3, 4), (1, 3), (1, 4), (5, 2)}

Let R be the relation

Then R = {(3, 4), (1, 3), (1, 4), (5, 2)}

Now domain of the relation

= { x : (x, y) ∈ R }

= { 1 , 3 , 5 }

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