##### For a regular expression e, let L(e) be the la...

For a regular expression e, let L(e) be the language generated by e. If e is an expression that has no Kleene star ∗ occurring in it, which of the following is true about e in general?

(A) L(e) is empty.

(B) L(e) is finite.

(C) Complement of L(e) is empty.

(D) Both L(e) and its complement are infinite.

##### 3Comments
Sumit Verma sumitverma 1 Dec 2016 03:52 pm

L(e) is finite. This is proved by a simple induction on the structure of the regular expression, using the fact that L(a) is finite for each letter a, and that unions and concatenations of finite languages are also finite.

Sumit Verma sumitverma 1 Dec 2016 04:59 pm

For every set L, the Kleene plus L+ equals the concatenation of L with L*. So if it is given that If e is an expression that has no Kleene star ∗ occurring in it, we can not talk about L+ .

Ananya Mukherjee ananyamukherjee 28 Jan 2018 09:45 am
@sumitverma Sir
why not C) is answer?
no kleenstar in the language means, language is a^+
So, complement of language is epsilon
isnot it?