Question

Let $A=\{a,b,c,d,e\},B=\{P,Q\}$ then number of onto function from $A$ to $B$ are

• A. $8$
• B. $6$
• C. $30$
• D. $32$

Answer 1

Answer: (C)

$30$

For every element of set $A$, there are two choices in set $B$.

Hence the number of function from set $A$ to set $B$ are $2^5$.
Out of these functions one function maps, all the elements of set $A$ are mapped to only one element, $a$ of set $B$. and the other function maps all the elements of set $A$ are mapped to the other element, $b$ of set $B$. Hence these two functions are not surjective. therefore the number of onto functions from set$A$ to set $B$ are $32-2=30$