Sloppy Sam is trying to prove a certain proposition P. He defines two related propositions and R, and then proceeds to prove four implications: RQ, QR, RP, P Q. He then reasons as follows If Q is true, then since I proved Q R, I can conclude that R is true. Now, since I proved R P, I can conclude that P is true. Similarly, if R is true, then P is true and so Q is true. Likewise, if P is true, then so are Q and R. So any way you look at it, all three of P, Q, and R are true. (a) Exhibit truth tables for and for (PQ) ^ (Q R) ^ (RP), (1) PAQAR. (2) Use these tables to find a truth assignment for P, Q, R so that (1) is T and (2) is F. (b) You show these truth tables to Sloppy Sam and he says "OK, I'm wrong that P, Q and R all have to be true, but I still don't see the mistake in my reasoning. Can you help me understand my mistake?" How would you explain to Sammy where the flaw lies in his reasoning?