For each of the following statements answer whether its true

For each of the following statements, answer whether it\'s true or false and justify your answer or you will receive no points. You may cite any language we proved to be regular or not regular in class as an example/counterexample without re-proving it, but if you use a language not proved in class, you must show that it\'s regular with a DFA/regex/grammar construction or show that it\'s not regular using the pumping lemma. If a DFA exists with 6 states that recognizes language L, a DFA must exist with 24 states that recognizes L. If an NFA exists with 6 states that recognizes language L, a DFA must exist with 24 states that recognizes L. If L* is regular, L is regular. If L_1 is regular, and L_1 o L_2 is regular, L_2 is regular. If L_1 L_2 is regular, at least one of L_1 or L_2 must be regular. If L_1 is regular, and L_2 is regular, L_1 - L_2 (the language of all strings that are in L_1 but not in L_2) must be regular.

Solution

a) Both divisible by 3 and 2 so the statement is True

b) Every NFA has equivalent DFA so this statements is False

c) A subset of a regular language not mandatory regular so this Statement is False

d) This Statement is True

e) this is true segment . Here L2 must be regular. So the Statement is True

f) this statement is True because l2 will be rejects.