You are given the following predicates and domain information:

variable x represents a student

variable y represents a course

C(x) : x is a CS major

T(x, y) : x is taking y

M(y) : y is a math course

F(x) : x is a Freshman

For each of the problems given write a statement using only the following:

predicates and variables listed above, quantifiers (, ), conditional (), connectives (, ), negation (), and parentheses. (You are NOT allowed to use , !, , nor anything beyond those expressly allowed.)

9.[5] Every math course has at least one CS major and at least one Freshman.

10.[5] Every Freshman is taking at least one math course.

11.[5] One or more Freshmen are CS majors.

12.[5] There are exactly two CS majors.

13.[5] There is a part-time student who is not taking any math course.