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.

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asked 2021-03-07
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.

Answers (1)

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.
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