Question

if n(A)=p, n(B)=q then total number of non-empty relations that can be defined from A to B is:​

Answer 1

Answer:

$\text{The total number of non-empty relations from A to B}=2^{pq}-1$  

Step-by-step explanation:

If n(A)=p, n(B)=q then total number of non-empty relations that can be defined from A to B is:​

$\text{Given: }$

$\text{n(A)=p and n(B)=q}$

$\textbf{Relation:}$

$\text{A relation from A to B is any non-empty subset of }A\times\,B}$

$\text{Clearly, the number of elements A\times\,B is pq}$

$\text{Then, the total number of relations from A to B}$

$=\text{The total number of subsets A\times\,B }$

$=2^{pq}$

$\text{Hence, the total number of non-empty relations from A to B}=2^{pq}-1$

Answer 2

The total number of non-empty relations that can be defined from A to B is $2^{pq}-1$.

Explanation:

Let P and Q are sets .

If n(P)= a and n(Q)= b , then n(P x Q)= ab

The total number of relations from P to Q = $2^{ab}$

Given : n(A)=p, n(B)=q

Then, the  total number of relations from A to B = $2^{pq}$

Since there is only one empty relation.

So the total number of non-empty relations from A to B=  $2^{pq}-1$

Hence, the total number of non-empty relations that can be defined from A to B is $2^{pq}-1$.

# Learn more :

List all the relations on the set A = {0,1}

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