The Agreement Dissection was split up into four parts, following a storyline that could only happen to Sheldon. The episode started with Sheldon running into Leonard and Priya in the bathroom, which Sheldon reacted later by pulling out the dreaded roommate agreement.
Sheldon's biggest dilemma with being a genius is his inability to accept the possibility that he does not have the answer to any given question. Worse yet, is when he is out-smarted not only by a magic trick, but also by Penny and the lowly master in engineering.
In Sheldon's mind, he believes that everything he says is perfectly acceptable, because he has deduced that it is right. He perceives himself as relying on his intelligence to be objective, however, his social incompetence makes him out of sync with the rest of the world.
Raj's sister, Priya (Aarti Mankad), was in town for one night on a layover. The back story of this episode involved a five year old agreement that Howard and Leonard made where they promised that nothing would happen between either one of them and Priya. By the evening, Priya had appeared at Leonard and Sheldon's door, while Sheldon was busy with a text based video game.