Question

I need help with discrete mathematics Let P(x) be the statement “Student x knows calculus” and let Q(y) be the statement “Class y contains a student who knows calculus.” Express each of these as quantification of P(x) and Q(y) .

a) Some students know calculus.
b) Not every student knows calculus.
c) Every class has a student in it who knows calculus.
d) Every student in every class knows calculus.
e) There is at least one class with no students who know