First slide

Functions (XII)

Question

The number of surjections from $A = \{1, 2 . . . ., n\}, n \geq 2$ onto $B = \{a, b\}$ is

Easy

A

${}^{n}P_{2}$
B

$2^{n} - 2$
C

$2^{n} - 1$
D

None of the these

Solution

$A = \{1, 2 . . . ., n\}, n \geq 2 B = \{a, b\}$
Number of into functions from A to B = 2
Total Number of functions from $A to B = {[n (B)]}^{n (A)} = 2^{n}$
$∴$ Total Number of onto functions from $A to B = 2^{n} - 2$

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