Let \(L_1 \), \(L_2 \) be two regular languages and \(L_3 \)a language which…

GATE · 2024 · CS · Set 1 · Computer Science & IT

Let L1L_1 , L2L_2  be two regular languages and L3L_3 a language which is not regular. Which of the following statements is/are always TRUE?

  1. A.

    L1=L2L_1 = L_2  if and only if  L1∩L2‾=𝜙 {L_1 \cap \overline{L_2}} = \text{𝜙}

  2. B.

    𝐿1 ∪ 𝐿3 is not regular

  3. C.

    L3‾\overline{L_3} is not regular

  4. D.

    L1‾∪L2‾\overline{L_1} ∪ \overline{L_2} is regular

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