Question

If n (A) = p and n (B) = q, then how many relations are there from A to B?​

Answer 1

SOLUTION

GIVEN

n(A) = p and n(B) = q

TO DETERMINE

The number of relations from A to B

CONCEPT TO BE IMPLEMENTED

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

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

RELATION :

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

EVALUATION

Here it is given that

n(A) = p and n(B) = q

Now n(A × B)

= n(A) × n(B)

= p × q

= pq

Hence the required number of relations from A to B

= The number of subsets of A × B

$\sf{ = {2}^{pq} }$

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