TITLE: How many relations are there between the set A and B?
QUESTION [7 upvotes]: $A =\{1,2,3\}$ and $B=\{a,b\}$
Based on the text, the number of relations between sets can be calculated using $2^{mn}$ where $m$ and $n$ represent the number of members in each set.
Given this, I calculated this number to be $2^{6}=64$ but this number seems too large.
Did I correctly calculate this value?

REPLY [4 votes]: The total number of relations that can be formed between two sets is the number of subsets of their Cartesian product.
For example:
$$
n(A) = p\\
n(B) = q\\
\implies n(AXB) = pq\\
Number\ of\ relations\ between\ A\ and\ B = 2^{pq}\\
$$
Remember that if $n(T) = m$, then the number of subsets of set $T$ will be $2^{m}$