Question: Solve 1. Let E(x,y) be the statement Student x is enrolled in course y. Express each of the following sentences in terms of E(x,y), quantifiers,

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1. Let E(x,y) be the statement "Student x is enrolled in course y.\" Express each of the following sentences in terms of E(x,y), quantifiers, and logical connectives, where the universe for x is the set of all students and for y is the set of all courses. (10 pts) (a) Every course has at least one student enrolled (b) There exists a student who is enrolled in all courses (c) Some student is enrolled in CMPSC 360 and CMPSC 311. (d) At least two different students are enrolled in the same course (e) There is a course that no student is enrolled in 2. Translate the following Predicate Logic to English sentences: (15 pts) (a) P(x): x is a professor. C(y): y is a course. T (x,y): x teaches y. Vy(C(y) + Ax(P(x) AT(x,y))) (b) P(x): x is a person. R(y): yis a party. A(x,y) + x attended y. vyax(R(y) (P(x) AA(x,9))) (c) N(x): xis a natural number. D(x,y) : x is divisible by y. xdy(N(x) (N(y) A D(x, y)))

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