Question

Which of the following statements about regular languages is NOT true?

• A. Every subset of a finite language is regular
• B. Every language has a regular superset
• C. Every language has a regular subset
• D. Every subset of a regular language is regular

Answer 1

The correct option is D Every subset of a regular language is regular

${\sum }^{\ast }$ is the regular superset of every language.

$\varphi$ is a regular subset of every language.

Every subset of a regular language is regular is false since $a^n{b}^n\subseteq {\sum }^{\ast },$ but $a^n{b}^n$ is not Regular but DCFL.

Since every subset of a finite language is finite and every finite set is regular. Hence, every subset of a finite language is regular.