Solve P14.2.5 and describe all of the distinguishable equivalence classes - how many are there?

42.4 A string in (a zl is said to be panalphabetic if it contains at least one occurrence of each letter. Examples of panalphabetic strings are thequickbrownfoxjumpsoverthelazydog and jackdawslovemybigsphinxofquartz. Is the language of panalphabetic strings decidable by a DFA? Prove your answer P142.5 A string in (a,...,z]* is said to be a palindrome if it is equal to its own reversal. Exam- ples of palindromes are madamimadam and ablewasiereisawelba. Is the set of palindromes decidable by a DFA? Prove your answer. P14.2.6 Following Exercise 14.2.4, let P2 be the subset of Paren that consists of strings where the excess of L's over R's in any prefix is never more than 2. Describe a DFA deciding P2, characterize the languages corresponding to each of its states, and prove your characterization correct