Question

If \(X=\{1,2,3\}\) and \(Y=\{a,b\}\), then find the number of functions from \(X\) to \(Y\).

Hint:

Number of functions from an \(m\)-set to an \(n\)-set is \(n^m\).

Answer 1

Step 1: General formula:
The number of functions from a set of size \(m\) to a set of size \(n\) is \(n^m\).

Step 2: Substituting:
Here \(m=|X|=3\), \(n=|Y|=2\), so the count is \(2^3\).

Final Answer:
\(2^3=\boxed{8}\) functions from \(X\) to \(Y\).