'John met the student' would translate as:
(∃x student(x) ⋀ (∀y (student(y) → y = x)) ⋀ met(j,x))
where, j stands for John.
We have the existential quantifier and the universal quantifier; hence, translation of 'a (or, some) student' and 'all students' would be easy but how could you express 'some students,' 'many students,' etc. in logical formulas?