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9. PS2.pdf CS 135 Spring 2018: Problem Set 2. Problem 1. (10 points) Let Fool(x, y,d) be a predicate that represents the statement "x makes a fool of y on day d." Thus, for example, 3x vd Fool(x, Lem,d) means that there is someone who fools Lem every day. Express each of the following statements as a quantified predicate. a. Every day Lem fools someone. b. There is a person who, on each day, fools someone other than himself c. Everyone fools someone someday. d. On any day a person who is fooled does not fool anyone that day. e. tem never fools himself. Now, let Wise(x), Future(d,d2) respectively denote the predicates "x is wise" and "on day di, day d2 lies in the future" (i.e, day d2 comes after day di). Use these in addition to Fool(x,y,d) to express the following statements f. A wise person never fools himself If Lem fools a wise person someday then he never fools that person on any future day. g. h. If someone fools Lem someday then Lem fooled himself someday in the past. Anyone who is fooled by the same person on more than one day is not wise. i. j. Lem was fooled two different people other than himself, each on a different day. Problem 2. (10 points) In this problem we explore the use of logic in computer arithmetic. As you know, computers represent numbers using the bits (binary digits) O and 1. These bits represent ively. The number two is represented