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CMI2021-A: 2

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Let $\text{L}$ be the language over $\left \{ a, b \right \}$ that contains the same number of occurrences of $a$ and $b$. Which of the following languages is regular?

  1. $\text{L} \cap  a^{\ast}b^{\ast}$

  2. $(\text{L} \cap  a^{\ast}b^{\ast}) \cup  a^{\ast}b^{\ast}$

  3. $\text{L} \cup  a^{\ast}b^{\ast}$

  4. $(\text{L} \cap  a^{\ast}b^{\ast}) \cup  b^{\ast}a^{\ast}$

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