Discrete mathematics question.

Explain in detail please

person(x)		x is a person.
short(x)		Person x is short.
tall(x)		Person x is tall.
taller(x, y)		Person x is taller than person y.

Answer the following questions by writing expressions in predicate calculus that use these predicates. Assume that quantified variables range over all possible objects, not just people, and not just people from Duosomata.

1. Write an expression that means Tall people are taller than short people.

2. Write an expression that means If there are any two people, and one is taller than the other, then the first person is tall, and the second person is short.

3. Write an expression that means At least one tall person is taller than any short person.

4. Suppose that this is true:

s t [person(s) person(t) short(s) tall(t) taller(s, t)]

Then prove that this is true:

s t [(person(s) person(t) short(s) tall(t)) taller(s, t)]

Your proof must be written as a series of steps. Each step must be an expression in predicate calculus. Each step (except the first one) must be derived from the previous step. You must give a reason for each step.