Question: 1. Is any language with finite number of strings regular? Is the langu

Question

Question:
1. Is any language with finite number of strings regular? Is the language of all strings regular?
2. Say that L is regular the set over 0, 1 Is the set, {x | x = 0y, y L} also regular?
3. For two regular languages, is M L = L M? Is it true if the alphabet is {0, 1}? Is it true if the alphabet is {0}?
4. 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, , d}. The suffix language of L is {, c, cb, cba, d}.

Explanation / Answer

1. Is any language with finite number of strings regular?
Ans: yes
Is the language of all strings regular?
Ans: No
2. Say that L is regular the set over 0, 1 Is the set, {x | x = 0y, y L} also regular?
Ans; Yes
3. For two regular languages, is M L = L M?
Ans: Yes
Is it true if the alphabet is {0, 1}?
Ans: Yes
Is it true if the alphabet is {0}?
Ans:Yes
4. If L is regular, is the language of all prefixes of L regular?
Ans: Yes
How about all the suffixes of L?
Ans: Yes
Example: If L = {abc, d} then the prefix language of L is {abc, ab, a, , d}. The suffix language of L is {, c, cb, cba, d}.

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