L₁=∅ and L₂=a. Evaluate L 1L 2* L 1*.

GATE 2013 CS (CS1) – Question 18

Theory of Computation · Regular Expressions and Finite Automata · 1 mark · Multiple choice

L₁=∅ and L₂={a}. Evaluate $L_1L_2^*\cup L_1^*$.

$\{\epsilon\}$
$\varnothing$
$a^*$
$\{\epsilon,a\}$

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Show answer and explanation

Correct answer: (A) $\{\epsilon\}$

Explanation

Concatenating the empty language with any language gives ∅, so L₁L₂*=∅. The Kleene star of ∅ is {ε}, because its zeroth power contains the empty word. Their union is {ε}, A.

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