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The number of functions from an $m$ element set to an $n$ element set is

  1. $m + n$
  2. $m^n$
  3. $n^m$
  4. $m*n$
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4 Answers

Best answer
35 votes
35 votes
No. of functions from an $m$ element set to an $n$ element set is $n^m$ as for each of the $m$ element, we have $n$ choices to map to, giving $\underbrace{n \times n \times \dots n}_{m \text{ times}} = n^m$.

PS: Each element of the domain set in a function must be mapped to some element of the co-domain set.
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7 votes

$m$ which is domain and $n$ which is co-domain ,so number of functions = $co-domain^{domain }$

so $n^{m}$

$OR$ In another way

Every element of Set with m elements have $n$ options so for $1\rightarrow n \space\text{for }2\rightarrow n$ options ,

Similiarly for $m\rightarrow n$ options so

$n\times n \times n \space ...\text{m times} = n^m$

So option $C$ Not $B$

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