Question

If $A=\{1,2,3\}$ and $B=\{4,5\}$ then the number of function $f:A\to B$ which is not onto is ______

• A. $2$
• B. $6$
• C. $8$
• D. $4$

Answer 1

The correct option is A $2$

Total number of function $f:A\to B$ is the number of relations from $A$ to $B$ such that all the elements of $A$ are in the first elements of function $f$.

Hence, total number of functions are $=2\times 2\times 2=2^3=8$

There are two functions for which the function is $\left\{\right(1,4),(2,4),(3,4\left)\right\}$ and $\left\{\right(1,5),(2,5),(3,5\left)\right\}$.

Hence there are two non-onto functions.