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Let A = {1, 2, 3, …..., n} and B = {a, b...

Let A = {1, 2, 3, …..., n} and B = {a, b}. Then the number of surjection from A into B is

A

`.^(n)P_(2)`

B

`2^(n)-2`

C

`2^(n)-1`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
B
`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`
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