Question

Let $A=${$1,2,3,4$} and $B=${$1,2$}. Then the number of onto functions from $A$ to $B$ is:

• A. $8$
• B. $14$
• C. $12$
• D. None of these

Answer 1

Answer: (B)

$14$

Since each element of $A$ can be associated with elements of $8$ in two ways,

therefore the total number of functions from $A$ to $B$ is

$2\times 2\times 2\times 2=16$

Out of these functions, the functions which are not onto are $f\left(x\right)=1,\forall x\in A$.

Thus, the number of onto functions $=16-2=14$.