6. The Curious Case of The Lying TAs (10 points) A new UW CSE student wandered around the Paul Allen building on their first day in the major. They found (as many do) that there is a secret room in its basements. On the door of this secret room is a sign that says: All ye who enter, beware! Every inhabitant of this room is either a TA who always lies or a student who always tells the truth! (a) [5 Points) The CSE student walked into the room, and two inhabitants walked up to the student. One of them said "at least one of us is a TA." Determine (with justification) all the possibilities for each of the two inhabitants. (b) (5 Points Three inhabitants walk up to the CSE student and surround the UW CSE student. One of them says "every TA in this circle has a TA to their immediate right." Determine (with justification) all the possibilities for each of the three inhabitants