Gate CS 2024 (1)| Question - 23 | Theory Of Computation & Automata

Let L₁, L₂ be two regular languages and L₃ a language which is not regular. Which of the following statements is/are alwaysTRUE?

$L_{1} = L_{2} i f a n d o n l y i f L_{1} \cap L_{2} = ϕ$

$L_{1} \cup L_{3} i s n o t r e g u l a r$

$L_{3} i s n o t r e g u l a r$

$L_{1} \cup L_{2} i s r e g u l a r$

Solution:

Option A: False, as a double implication we need to check both sides and take a case where L₁ is a subset of L₂ still, the intersection of the statement will be null.

Option B: False, take L₁ as (a+b)*, the union of any non-regular language over alphabet a and b with language L₁ will always be regular.

Option C: True, Regular languages are closed under complementation.

Option D: True, Regular languages are closed under union.

Learn more about Closure Properties.

Gate CS 2024 (1)| Question - 23 | Theory Of Computation & Automata

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