Question #1.

Question

1. Say that L is regular over 0, 1. Is the set, {x|x = 0y,y ∈L } also regular?

2. For two regular languages
(a) Is M*L=L*M for any alphabet?
(b) Is it true if the alphabet is only {0,1}?
(c) Is it true if the alphabet is only {0}?

3. If L is regular, is the language of all prefixes of L regular? How about all the suffixes of L?
Example: If L={abc,d} then the prefix language of L is {abc,ab,a,e,d}. The suffix language of L is {e,c,cb,cba,d}.