Question

a relation from A to B is an arbitrary subset of:
a)A×B
b)B×B
c)AxA​

Answer 1

Answer:

relation from a set A to a set B is a subset of A×B. A (binary) relation on A is a subset of A × A. It is important to remember that a relation is a set or ordered pairs. There need be no relationship between the components of the ordered pairs; any set of ordered pairs is a relation.

Answer 2

A relation from A to B is an arbitrary subset of A × B

Given :

A relation

To find :

A relation from A to B is an arbitrary subset of

a) A × B

b) B × B

c) A × A

Solution :

Step 1 of 2 :

Define relation

To define relation we define cartesian product

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 relation is defined as below

Let A and B are two non empty sets. Then a Relation R from A to B is a Subset of A × B

Step 2 of 2 :

Choose the correct option

Here the given sets are A and B

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

Hence the correct option is a) A × B

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