GATE CSE 1987 | Question: 2i

Question

State whether the following statements are TRUE or FALSE:

All subsets of regular sets are regular.

Comments

1. Every finite subset of a non-regular set is regular.
2. Every finite subset of a regular set is regular.

Answer 1

False!
$a^*b^*$ is regular but its subset $a^nb^n$ is not regular.

Comments

yes.

---

Finite subsets of regular sets are regular.

---

Finite subsets of regular sets are regular.

Sumaiya23

A finite subset of any non regular set is also regular, right !. As every finite set is regular.

Answer 2

$\sum ^{*}$ is regular which contains every language such as a $a^{n}b^{n}$ which is non regular. 

Therefore, Regular Languages are not closed under subset.