Question

Convert the following sentences into symbolic form. i) All planets revolves around sun in an elliptical orbit ii) No student who is intelligent will fail.

Answer 1

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