Question

The number of possible surjection from $A=\{1,2,3,...n\}$ to $B=\{1,2\}$ (where $n\ge 2)$ is $62$, then $n=$

• A. $5$
• B. $6$
• C. $7$
• D. $8$

Answer 1

Answer: (B)

$6$

Each element in $A$ can be mapped onto any of two elements of $B$
$\therefore$ Total possible functions are $2^n$
For the $f^{n^{\prime }s}$ to be surjections , they shouldn't be mapped alone to any of the two elements.
$\therefore$ Total no of surjections $=2^n-2$
$2^n-2=62$
$\Rightarrow n=6$