If $A=\{a,b\}$ and $B=\{c,d\}$, how many relations can be defined from $A$ to $B$?

Solution

1. The number of elements $n(A)=2$ and $n(B)=2$.
2. The number of elements in the Cartesian product $A\times B$ is $2\times 2=4$.
3. The total number of relations is $2^{n(A\times B)}=2^4$.
4. $2^4=16$.
5. Hence the answer is (C).