Question

Write the following statement in symbolic form using quantifiers:
I. All students have taken a course in Mathematics
II. Some students are intelligent, but not hardworking.

Answer 1

I. All students have taken a course in Mathematics

$(\forall x)[S(x) \mapsto M (x)]$

S(x): x is a student

M(x): x have taken a course in Mathematics 

II. Some students are intelligent, but not hardworking.

$(\exists x)(I(x)\land [H(x)]')$

S(x): x is a student

I(x): x is intelligent

H(x): x is hardworking