Problem Set 1 roblem 1. [24 points] Translate the following sentences from English to predicate logic. The domain that you working over is X, the set of people. You may use the functions S(x), meaning that "x been a student of 6.042," A(x), meaning that "x has gotten an 'A' in 6.042," T(x), meani that "x is a TA of 6.042," and E(x, y), meaning that "x and y are the same person." (a) [6 pts] There are people who have taken 6.042 and have gotten A's in 6.042 (b) [6 pts] All people who are 6.042 TA's and have taken 6.042 got A's in 6.042 (c) [6 pts] There are no people who are 6.042 TA's who did not get A's in 6.042. d) [6 pts] There are at least three people who are TA's in 6.042 and have not taken 6.042 oblem 2. [24 points] a truth table to prove or disprove the following statements: 12 pts] -(PV (QAR)) = (-P) ~(-Q V - R) ots] - (P A (Q V R)) = - PV(-Q V-R) 739 MAY 29