Testbook Chapter Test on Finite Automata (CT: 19)

Question

Which of the following statements is/are true?

1. The language denoted by the regular expression (ϕ*)* is ϵ
2. The language denoted by the regular expression a ϕ is ϕ
3. The regular expression for the language L={vuv|v,u∈{a,b}*,|v|≤3 } is L=(a+b)*
4. The language denoted by the regular expression (ϕ*)* is ϕ

 

The correct answer is option 1, option 2, and option 3.

How can 1 be true? Since, phi (ϕ) denotes an empty set, zero or more combinations of it will still denote an empty set, right?  Whereas, epsilon (ϵ) is not an empty set.

 And option 4 is True, right?

Comments

ϕ*  = ϕ⁰ + ϕ¹ + ... = ϵ + ϕ +... = ϵ