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The definition of a language $N$ with alphabet set $\left \{ x \right \}$ is given below:

$N= \{ x^{mp} \mid p > \: 0, \text{where m is a positive integer constant} \}$

The minimum number of states needed in a $\text{DFA}$ to recognize $N$ is _________.

  1. $p+m$
  2. $p+1$
  3. $m+1$
  4. $2^\left ( p+1 \right )$
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Let's assume $m=2,p=1$ so, $x^{2\times1}=x^2$ 

so minimum number of states = (2+1) = $m+1$

Hence $Option \space C$

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