# Question: for each of the following statements state whether it is...

###### Question details

For each of the following statements. state whether it is True or False. Prove your answer: a. ∀L1 , L2(L1= L2)iff L1*·=L2*). b. (ØuØ*)n(¬Ø- (ØØ*)) = Ø (where ¬Ø is the complement of Ø). c. Every infinite language is the complement of a finite language. d. ∀L ((LR)R = L). e. ∀L1, L2((L1L2)*= L1*L2*). f. ∀L1, L2(( ((L1*L2*L1*)*= (L2UL1)*). g . ∀L1, L2(( ( ( L 1 U L 2 ) * = L 1 * U L 2 * ) . h. ∀L1, L2((,L3((L1UL2)L3= (L1L3)U(LzLJ)). i. ∀L1, L2, L3 ((L,L2) U L3 = (L1U L3) (L2 U L3)) j. ∀L ((L+)* = L*). k. ∀L (ØL* = {e}). I. VL(ØUL+= L*). m. VL1, L2 ((L1 U L2)* = (L2 U L1)*). the * indicates the set of possible strings. The set of all possible strings over an alphabet is indicated by Σ* L consists of all strings that can be formed by taking some strings in {a,b}* Where a, b are elements of L and some psossible strings that can be formed include, a, aa, bb, aaabb, etc.