Question-44

Let \(\displaystyle A=\{1,2,3,4,5\}\) and \(\displaystyle B=\{1,-1\}\). Find the number of functions from \(\displaystyle A\) to \(\displaystyle B\).

Answer

\(32\)

Solution

Each value in the domain can be mapped to one of two values in the co-domain:

\[ \begin{equation*} 2\times \cdots \times 2=2^{5} \end{equation*} \]

We can define \(\displaystyle 32\) functions between \(\displaystyle A\) and \(\displaystyle B\).