Question

If a set A has m elements and set B has n elements then the number of relation from A to B is
​

Answer 1

Answer:

If there are n elements in the set A and m elements in the set B, then there will be (nxm) elements in AxB . Accordingly, there will be 2^(nxm) subsets of AxB and therefore there can be defined 2^(nxm) relations from A to B .

Step-by-step explanation:

Answer 2

SOLUTION

TO DETERMINE

If a set A has m elements and set B has n elements then the number of relation from A to B is

EVALUATION

We know that set is a well defined collection of distinct objects of our perception or of our thought to be conceived as a whole

Now cartesian product is defined as below

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

Here it is given that A has m elements and set B has n elements

Thus we have n(A) = m and n(B) = n

Now the number of elements in A × B

= n( A × B )

= n(A) × n(B)

= m × n

= mn

Hence the number of relation from A to B

$\sf = 2^{mn}$

FINAL ANSWER

If a set A has m elements and set B has n elements then the number of relation from A to B is $\bf 2^{mn}$

━━━━━━━━━━━━━━━━

Learn more from Brainly :-

$1.$ identify distinction between a relation and a function with suitable examples and illustrate graphically

https://brainly.in/question/23643145

2. Represent all possible one-one functions from the set A = {1, 2} to the set B = {3,4,5) using arrow diagram.

https://brainly.in/question/22321917