Translate the following into predicate logic: Suppose you have the following predicate: P(xy) means x+2yex*y", where x and y are integers. Determine whether the following statements are true or false: 1. 2. Suppose you have the following: U(): y is an upper-level course, M):y is a math course, Fx): x is a freshman, B(x): x is a full-time student Toxy): student x is taking course y, A(x): is a part-time student. Note that here I used x to represent a student and y to represent a course. Translate the following into predicate logic: a. No math course is upper-level b. Every freshman is a full-time student c. Fran is taking MTH 281 d. There is a part-time student who is not taking any math course e. Every part-time freshman is taking some upper-level course f. Some student is taking every course g. Every full-time freshman is taking a math course 3. Suppose you have the following: the variables x and y represent real numbers, and Uxy) : x 0 P(x) : x is a prime number. Q(xy) : x-y even, Ix): x is an integer. Translate into predicate logic: E(x) : x is a. There is no largest number b. No matter what positive number is chosen, there is a larger prime c. Ifx