If n(A) = 3, n(B) = 2, then number of all possible surjective function from set A to set B are:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
Each of the 3 elements of A can go to either of the 2 elements of B, so the total number of functions from A to B is
\(2^3 = 8\)
A function is surjective (onto) when every element of B is an image. The only functions that are not onto are the two constant functions, which send all of A to one element of B. So
\(\text{number of onto functions} = 8 - 2 = 6\)