##### 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. |

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.

For every set

L, the Kleene plusL^{+}equals the concatenation ofLwithL^{*}. So if it is given thatwe can not talk aboutIf e is an expression that has no Kleene star ∗ occurring in it,L^{+}.why not C) is answer?

no kleenstar in the language means, language is a^+

So, complement of language is epsilon

isnot it?