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) → \(2^n-2\)
Each of the n elements of A can go to x or to y, so the number of functions from A to B is
\(2 \times 2 \times \dots \times 2 = 2^n\)
A function is not onto only if it misses x or misses y, that is, if it sends every element to y, or every element to x. These are 2 functions, so
\(\text{number of surjections} = 2^n - 2\)
NCERT Exemplar:
Relations and Functions
