Question: Problem 2. (15 points) Let Loves(x, y, d) be the predicate X loves y on day d. Thus, for example, 3x Vd Loves(x.Juliet, d) means

Problem 2. (15 points) Let Loves(x, y, d) be the predicate

Problem 2. (15 points) Let Loves(x, y, d) be the predicate "X loves y on day d." Thus, for example, 3x Vd Loves(x.Juliet, d) means that there is someone who loves Juliet every day. a. (1 point) What are the domains of variables x and d in the example above? Express each of the following statements as a quantified predicate (2 points) Every day Juliet is loved by someone. (3 points) lago never loves himself. b. C. Now, let Future(d1,d2) denote "day d1 comes before day d2." Also let EQ(x, y) denote "x and y are the same person" and EQ(d1, d2) denote "day dis the same as d2." Use these in addition to Loves(x, y, d) to express the following statements. (3 points) There is a person who, on each day, loves someone other than himself. (3 points) Everyone who someday loves a person who loves everyone everyday loves that person ever after. (3 points) No one loves anyone on days when they are not loved by anyone else. (Extra Credit 5 points) Anyone who loves one person one day, and on a later day loves someone else but not the person he loved the first day is not loved after the later day by the person he loved earlier d. e. f. g

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