Question

# We have a set of n-elements (A), and a set of m-elements (B). n>=0 m>=0 Find how many relations there're from A to B.

Data distributions
We have a set of n-elements (A), and a set of m-elements (B).
$$\displaystyle{n}\ge{0}$$
$$\displaystyle{m}\ge{0}$$
Find how many relations there're from A to B.

2021-03-08
If A can occur in n ways and B can occur in m ways, than A and B in a sequence can occur in mn ways.
For each of the nm pairs, there're 2 options: in the relation and not in the relation.
1st pair: 2 ways
2nd pair: 2 ways
...
nmth pair: 2 ways
Thus, there are $$\displaystyle{2}^{{{n}{m}}}$$ relations from A to B.