Professor Carlson's class in mechanics is comprised of 29 students of which exactly
(1) Three physics majors are juniors;
(2) Two electrical engineering majors are juniors;
(3) Four mathematics majors are juniors;
(4) Twelve physics majors are seniors;
(5) Four electrical engineering majors are seniors;
(6) Two electrical engineering majors are graduate students; and
(7) Two mathematics majors are graduate students.
Consider the following open statements.
c(x): Student x is in the class (that is, Professor Carlson's mechanics class as already described).
j(x): Student x is a junior.
s(x): Student x is a senior.
g(x): Student x is a graduate student.
p(x): Student x is a physics major.
e(x): Student x is an electrical engineering major.
m(x): Student x is a mathematics major.
Write each of the following statements in terms of quantifiers and the open statements c(x), j (x), s(x), g(x), p(x), e(x), and m(x), and determine whether the given statement is true or false. Here the universe comprises all of the 12,500 students enrolled at the university where Professor Carlson teaches. Furthermore, at this university each student has only one major.
(a) There is a mathematics major in the class who is a junior.
(b) There is a senior in the class who is not a mathematics major.
(c) Every student in the class is majoring in mathematics or physics.
(d) No graduate student in the class is a physics major.
(e) Every senior in the class is majoring in either physics or electrical engineering.