If $A = \{1,2,3,4,...,n\}$ and $B = \{x, y\}$, then the number of surjections from A to B is

$2^n-2$

The correct answer is Option (2) → $2^n-2$

Given: $A = \{1,2,3,4,\ldots,n\},\quad B = \{x, y\}$

Number of functions from $A$ to $B = 2^n$

Number of non-surjective functions = functions mapping all $n$ elements to only $x$ or only $y$ = $2$

Number of surjections = $2^n - 2$