Problem 1

(a) Let x denote a student, S(x) denote that x is a student of Discrete Structures, C(x) denote x is Chinese, F(x) denote x is French, SF(x) denote x speaks French, and SC(x) mean x speaks Chinese. Then express the following sentences in Predicate Logic: In the Discrete Structures class, some Chinese students speak French, but no French student speaks Chinese.

(b) Let L(x) denote x won the lottery, and P(x) denote x joins the party. Then express the following sentence in Predicate logic: If anyone wins the lottery then everyone joins the party.

(c) Let the predicate M(y) denote y is a math course, A(x) denote x is a part-time student, and T(x, y) denote student x is taking course y. Then write the following statement using these predicated and the necessary quantifiers. There is a part-time student who is not taking any math course.

(d) Assume that the universe for x is all people and the universe for y is the set of all movies. Also, let S(x, y) denote x saw y L(x, y) denote x liked y A(y) denote y won an award and C(y) denote y is a comedy. Then write the English statement using the following predicates and any needed quantifiers: (i) No comedy won an award (ii) Some people have seen every comedy