Problem 3. (15 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, 3a: Vb: Fool(a, Lem, b) means that there is someone who fools Lem every day. Express each of the following statements as a quantified predicate. (3 points each) 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. Lem never fools himself