Question

Mark the correct alternative in the following question:

Let A = {1, 2, ... , n} and B = {a, b}. Then the number of subjections from A into B is

(a) ⁿP₂ (b) 2ⁿ $-$ 2 (c) 2ⁿ $-$ 1 (d) ⁿC₂

Answer 1

As, the number of surjections from A to B is equal to the number of functions from A to B minus the number of functions from A to B whose images are proper subsets of B.

And, the number of functions from a set with n number of elements into a set with m number of elements = mⁿ

So, the number of subjections from A into B where A = {1, 2, ... , n} and B = {a, b} is 2ⁿ $-$ 2. (As, two functions can be many-one into functions)

Hence, the correct alternative is option (b).