Consider the languages L and L: L = {ww | w ∈ {a,b}∗}, all even-length strings of as and bs whose first and second halves are equal, and its complement L = {w | w ∈ {a,b}∗ ∧ w 6∈ L}, all strings of as and bs that are not in L. One of these languages is a CFL and the other is not. Either show that L or L̅ is context free by giving (design and formalize)

Let regular language L1 recognized by DFA (Q1,Σ,δ1,s1,F1) and regular language L2 recognized by DFA (Q2,Σ,δ2,s2,F2). We will construct a product DFA as the quintuple (Q,Σ,δ,s,F) where: •Q=Q1×Q2•For allx∈Σ and (q1,q2)∈Q1×Q2,δ((q1,q2),x) = (δ1(q1,x),δ2(q2,x))•s= (s1,s2) DetermineFso that the product DFA recognizes: (i)L1∪L2(ii)L1∩L2(iii)L1\L2Based on your choice for F, for each case, provide a detailed proof why the product DFA recognizes each of the mentioned languages. Conclude that in-tersection of two regular languages is a regular language and set-theoretic dif-ference of two regular languages is regular.

Question 5 Let I be the set of all even length binary strings. (So I is decidable.) Give an example of a language K ⊆ I with K undecidable. Here you need to define the set K and state your reasoning why the K you define is undecidable. Full explain this question very fast solution sent me step by step text typ work only