# Confusion regarding regular language

A regular language is a language that can be represented by a regular expression(or for which there exists a DFA), then why is language represented by 0$^{+}$ not regular?

I am asking this because for the following question the correct answer is option 2

Let L denote the languages generated by the grammar S→0S0∣00. Which of the following is TRUE?

1. L=0$^{+}$

2. L is regular but not 0$^{+}$

3. L is context free but not regular

4. L is not context free

• Because $L$ it is regular and it is not $00^*$ but $00(00)^*$, so this refers to $L$ being a different language, not to deny that $0^+$ is regular? – Evil Oct 12 '17 at 14:57
• @Evil My bad, english is not my native language. – Sumeet Oct 12 '17 at 15:04
• Please give a reference for the problem you quote. – Raphael Oct 12 '17 at 16:25

The statement (2) is ambiguous. It could mean either $$L \text{ is regular but } L \text{ is not equal to } 0^+ \tag{1}$$ Or it could mean, $$L \text{ is regular but } 0^+ \text{ is not regular} \tag{2}$$ (1) is true and (2) is false. The authors of the question intended it to mean (1). But you thought that the meaning was (2), so you were confused.