Prove or disprove the following a If Lis regular then L must

Prove or disprove the following:

(a) If L*is regular, then L must be regular.

(b) For any language L, L* must be regular.

(c) If L1L2 is regular, then both L1 and L2 have to be regular.

(d) The union of finite number of regular languages is always regular.

(e) The union of infinite number of regular languages is always regular.

Solution

(a).

(b).

^(c).

^(d).

^(e).