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A new CSE student wandered around the engineering building on their first day in the major. They found (as many do) that there is a secret room in...

A new CSE student wandered around the engineering 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! 

(1) 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.

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