Question

The number of relations from $A=\{2,6\}$ to $B=\{1,3,5,6,7\}$ that are not functions from A to $B$ is

Answer 1

According to the problem, $|A|=2$ and $|B|=5$.

Now number of relations from the set $A$ to $B$ is $2^{2\times 5}=2^{10}$.

Also number of mappings from the set $A$ to $B$ is $5^2$.

So number of relations from $A$ to $B$ that are not functions is $2^{10}-5^2=1024-25=999$.