Consider the following two languages over the alphabet \(\{𝑎, 𝑏\}\): \(L_1 =…

GATE · 2025 · CS · Set 1 · Computer Science & IT

Consider the following two languages over the alphabet {𝑎,𝑏}\{𝑎, 𝑏\}:

L1={αβα∣α∈{a,b}+ AND β∈{a,b}+}L2={αβα∣α∈{a}+ AND β∈{a,b}+}L_1 = \{ \alpha \beta \alpha \mid \alpha \in \{a, b\}^+ \text{ AND } \beta \in \{a, b\}^+ \} \\ L_2 = \{ \alpha \beta \alpha \mid \alpha \in \{a\}^+ \text{ AND } \beta \in \{a, b\}^+ \}

Which ONE of the following statements is CORRECT ?

  1. A.

    Both L1L_1 and L2L_2 are regular languages.

  2. B.

    L1L_1 is a regular language but L2L_2 is not a regular language.

  3. C.

    L1L_1 is not a regular language but L2L_2 is a regular language.

  4. D.

    Neither L1L_1 nor L2L_2 is a regular language.

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