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Which of the following regular expressions defines a language that is different from the other choices?

  1. $b^{\ast }\left ( a+b \right )^\ast a\left ( a+b \right )^ \ast ab^\ast \left ( a+b \right )^{\ast }$
  2. $a^{\ast }\left ( a+b \right )^{\ast }ab^{\ast }\left ( a+b \right )^{\ast }a\left ( a+b \right )^{\ast }$
  3. $\left ( a+b \right )^{\ast }ab^{\ast }\left ( a+b\right )^{\ast }a\left ( a+b \right )^{\ast }b^{\ast }$
  4. $\left ( a+b \right )^{\ast }a\left ( a+b\right )^{\ast }b^{\ast }a\left ( a+b \right )^{\ast }a^{\ast }$
  5. $\left ( a+b \right )^{\ast }b^{\ast }a \left ( a+b\right )^{\ast }b^{\ast }\left ( a+b \right )^{\ast }$
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Language of options $(a),(b),(c)$ and $(d)$ is the set of strings over $\{a,b\}$ containing at least two $a’s$.

Language of option $(e)$ is the set of strings over $\{a,b\}$ containing at least one $a$.
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Option E is the answer  Bcz only 1 a  {a} as a minimum string is getting

in option A,B,C,D Minimum 2 a string {aa}
Answer:

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