Writing a sentence using predicates

Question

• I(x) = "x is a person"
• T(x,y) = "x is smarter than y"
• M(x) = "x is a mathematician"
• A(x) = "x can calculate"

I need to write two sentences using these:

• a) Every person who can calculate is smarter than every person who can't
• b) Every person, who is smarter than someone who can calculate, is smarter than some mathematicians.

I was able to write previous ones, but I'm having trouble with these.

Answer 1

For (a), $\phi_1 = \forall x \forall y (I(x) \land I(y) \land A(x) \land \lnot A(y) \implies T(x,y))$.

And for (b), $\phi_2 = \forall x (\exists y (I(x) \land T(x,y) \land A(y) )\implies \exists z (M(z) \land T(x,z)))$.