Answer the following. Assume that regular languages are closed under union, intersectton, a icent operation. Also, assume that CFL's are closed under union and concatenation operation. tLIS a regular language over some alphabet , then prove/disprove that L{xyz X, Z e L and y e LL} 1S a1so regular. To prove/disprove, use only closure properties of regular languages. b) For languages A and B, let the perfect shuftle of A and B be the language ddia,b:.. a,bk, where aja...a e A, bib..by e B, each a, b, e }, Complete the following proo to show that the class of regular languages is closed under perfect shuftle. Let DA (QA2, a. SA, Fa) and Da= (QB. , n, Sn, FR) be the DFA's accepting A and B respectively Construct a DEA D= (Q. ,8, s, F) that recognizes the required strings. So, formally, DFAD can be defined as: QAXQ8 NX, Y}. It keeps track of all possible current states of DA and DB, and which DFA to match. Mathematically define the start state, set of final states, and transition function of D. C)Assume that R is a regular language. Prove/disprove that R'= {x ER|x does not belong to R} is also regular (where is defined as the reverse ofx). To prove/disprove, use only closure properties of regular languages. d) Let Li, La, and La be languages defined over the alphabet fa, b}, where Li consists of all possible strings overexcept the strings Wi, W2, strings over the alphabet, take out 100 particular strings, and the remaining strings form the language LI La is recognized by an NFA; and La is recognized by a PDA What type of language is (L N L2) Ls? Prove your answer using only closure properties.