GATE CS 1987 Q2i — Regular and Context-free Languages

The statement is FALSE (represented by 0).

Explanation:

A language is regular if it can be recognized by a finite automaton. However, a subset of a regular language does not necessarily inherit this property.

We can prove this with a simple counterexample:

1. Let $\Sigma = \{a, b\}$. The set of all strings over $\Sigma$, denoted as $\Sigma^* = \{a, b\}^*$, is a regular language.
2. Consider the subset $L = \{a^n b^n \mid n \ge 0\}$.
3. Clearly, $L \subseteq \Sigma^*$.
4. However, $L$ is a well-known non-regular language (it requires memory to match the number of $a$'s and $b$'s, which cannot be done by a finite automaton).

Since we found a subset of a regular set that is not regular, the given statement is false.