GATE CSE 2024 Session 1 Q23: Closure facts for regular and non-regular languages

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?

Try it: multiple select: one or more correct options

Select all correct options. No negative marking, no partial marks.

Show answer and explanation

Answer: C, D (official GATE 2024 final answer key)

Concept used: Regular languages are closed under complement and union; a non-regular language's complement is non-regular.

First step: Test (B) with $L_1 = \Sigma^*$ , and note that $L_1 \cap \overline{L_2} = \phi$ only says $L_1 \subseteq L_2$ .

Full step-by-step solution

Detailed working, common mistakes and linked mock tests will be available with a free GATEiit account. Log-in is coming soon.

Share this question

Source: official GATE 2024 Session 1 CS question paper and final answer key, organised by IISc Bangalore. Question paper · Answer key