Let `A={1,\ 2,\ ,\ n}` and `B={a ,\ b}` . Then the number of subjections from `A` into `B` is `\ ^n P_2` (b) `2^n-2` (c) `2^n-1` (d) `\ ^n C_2`

Options

A. `.^(n)P_(2)`
B. `2^(n)-2`
C. `2^(n)-1`
D. None of these

Answer

B

Explanation

`A = {1, 2, …,n} n ge 2`
B = {a, b}
Number of into functions from A to B = 2
Total Number of functions from A to B = `[n(B)]^(n(A))=2^(n)`
`therefore` Total Number of onto functions from A to B = `2^(n) - 2`