Question

Express this statement using quantifiers: "Every student

in this class has taken some course in every department

in the school of mathematical sciences."

Answer 1

Let s represents student, d - department, c - course,

S - set of students of the class,

D - set of departments of the school of mathematical sciences,

C(d) - set of courses of the department d,

P(s, c) means "Student s has taken course c"

Our statement expression:

$\forall s\in S\space\forall d\in D\space\exist c\in C(d)\space P(s,\space c)$