Design a deterministic finite state automaton (DFA) that accepts exactly the strings over the alphabet {A, B, ...,Z} that contain at least two R, at most one T, and where every E comes after some S (there may be other letters in between). For instance, your DFA should accept the strings: • MYSTICWARRIORS • MARSMATRIX • SHOCKTROOPERS • CONTRAHARDCORPS STRIDER but not the strings • CRAZYTAXI (it does not contain at least two Rs) LASTRESORT (it contains more than one T) AFTERBURNER (there are Es without a S somewhere before them) • BATTLECIRCUIT (all of these at the same time) Clearly indicate the meaning of each state. One way to do this is to number the states and have a numbered list of their meanings, but any readable method you use to label and explain your states is fine. Hint: there are three separate conditions accepted strings must meet; states will need to encode whether or not each one is met (or perhaps partially met). You can label an edge with the word “else" to indicate it…

Define the Functor class and explain the idea of a Functor. Give an example of a Functor for a binary tree with data stored in nodes and leaves as part of your answer: data Tree a = Leaf a | Node a (Tree a) (Tree a) Tree a = Leaf a | Node a (Tree a) Tree a = Leaf a | Node a (T (200 words max. without code).

Suppose a tree generated by a compound proposition X has only closed paths. Does this mean that X is a contradiction? Please explain your answer. *Suppose a tree generated by a compound proposition Y has only open paths. Does this mean that Y is a tautology? Please explain your answer.