Question

Let A = {a, b}. Then number of one-one functions from A to A possible are

Answer 1

The number of possible one-one functions from A to A are 2

Given :

The set A = {a, b}

To find :

The number of possible one-one functions from A to A

Solution :

Step 1 of 2 :

Write down the given set

The given set is A = {a, b}

Step 2 of 2 :

Find number of possible one-one functions from A to A

Number of elements in A = 2

So the number of possible one-one functions from A to A

$\displaystyle \sf{ = {}^{2}P_2 }$

$\displaystyle \sf{ = \frac{2 \: !}{(2 - 2)!} }$

$\displaystyle \sf{ = \frac{2 !}{0!} }$

$\displaystyle \sf{ = 2}$

The two possible one - one functions are

{ (a, a) , (b, b) } & { (a, b) , (b, a) }

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