2. (1 pt) Let x and y be two words (both different than the empty string) and xy is their concatenation. Show that if x, y and xy are all in PALINDROME, then there is a word z such that x=z" and y=z" for some integers n and m. 3. (1 pt) Let S={ab, bb} and T={ab, bb, bbb}. Show that S*T* but that S*ct*. 4. (1 pt) Write the regular expression for the language of all strings, over alphabet {a, b}, that end in a double letter, i.e. ending in aa or bb but not ab or ba 5. (1 pt) Draw Deterministic Finite Automata to accept the following sets of strings, over the alphabet {0,1}, that contain exactly four Os (not necessarily consecutive zeros) Extra Credit: (1 pt) Write the regular expression for the language of all strings, over alphabet {0, 1}, the set of all strings in which every pair of adjacent zeros appears before any pair of adjacent ones. Justify