If $A = \{1,2,3,4,...,n\}$ and $B = \{x, y\}$, then the number of surjections from A to B is
Answer & explanation
Correct answer: option 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 = $2^n - 2$