Let \(L_1 \), \(L_2 \) be two regular languages and \(L_3 \)a language which…
2024
Let \(L_1 \), \(L_2 \) be two regular languages and \(L_3 \)a language which is not regular. Which of the following statements is/are always TRUE?
- A.
\(L_1 = L_2 \)if and only if\( {L_1 \cap \overline{L_2}} = \text{𝜙}\) - B.
𝐿1 ∪ 𝐿3 is not regular
- C.
\(\overline{L_3}\)is not regular - D.
\(\overline{L_1} ∪ \overline{L_2}\)is regular
Attempted by 137 students.
Show answer & explanation
Correct answer: C, D
Correct statements:
The complement of L3 is not regular.
Reason: Regular languages are closed under complement. If complement(L3) were regular, then L3 would be the complement of a regular language and thus regular, contradicting the hypothesis that L3 is not regular.
The union of complement(L1) and complement(L2) is regular.
Reason: L1 and L2 are regular, so complement(L1) and complement(L2) are regular (closure under complement). The union of two regular languages is regular (closure under union), so complement(L1) ∪ complement(L2) is regular.
A video solution is available for this question — log in and enroll to watch it.