Question

1. show abbabaab ∈ L(G) ------------- L = {ww^r : w ∈ {a, b}*}

Answer 1

L = {ww^r : w ∈ {a, b}*}

Given language says that it must consists of word that has a string w and and w^r means every letter must be reversed letter of w.

Given string is "abbabaab". Length of word is 8.

Since length of w and w^r is same, so we can partition the given word exactly at 4, so w1=abba and w2=baab.

And every letter in w2 is revered letter of word present on w1 in respective indices, wecan say that w2 is w^r of w1.

So, we can say that w=abba and w^r=baab

So ww^r = abbabaab will definitely belongs to given language.

Mention in comments if any mistakes or errors are found. Thank you.