Question

if n(a)=p and n(b)=q then the total number of relations that exist between a and b is 2↑{pq}

Answer 1

Answer:

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

Step-by-step explanation:

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