Let the universe of discourse consist of all students in you

Let the universe of discourse consist of all students in your class.

Let, x: students

y: courses

F(x): “x is a Freshman”

C(x): “x is a Computer Science major”

M(y): “y is a math course”

T(x, y): “x is taking y Express the statements below in terms of the given predicates defined above, quantifiers and logical connectives.

(a) Ben is a Computer Science major.

(b) Some Freshman is taking Calculus 3.

(c) Every Computer Science major is taking at least one math course.

(d) Every course has a student in it who is not a Math major.

(e) No Freshman is taking every math course.

Solution

Let, x: students y: courses F(x): “x is a Freshman” C(x): “x is a Computer Science major” M(y): “y is a math course” T(x, y): “x is taking y Express the statements below in terms of the given predicates defined above, quantifiers and logical connectives. (a) Ben is a Computer Science major. C(Ben) (b) Some Freshman is taking Calculus 3. x(F(x) T(x, Calc3)) (c) Every Computer Science major is taking at least one math course. x(C(x) y(M(y) T(x, y))) (d) Every course has a student in it who is not a Computer Science major. yx(T(x, y) ¬C(x)) (e) No Freshman is taking every math course. ¬x(F(x) y(T(x, y) M(y)))