How Is Predicate Calculus Used to Formalize Mathematical Statements?

[majeedh]

if the problem is asking :

express the problem in first
order predicate calculus. The Universe of Discourse
for all variables is “anything”

what does this mean? what are they asking for?

the problem they are referring to is to prove that if n is a positive integer, thenn is even if and only if 7n + 4 is even ( which i solved)

 

[honestrosewater]

It sounds like they want you to translate the English statements in your proof into statements in first-order predicate calculus that have the same meaning. What's the first statement, your one assumption?

n is a positive integer.

Do you know one way to express that in FOPC?

I think the Universe of Discourse part is there to specify that they don't want you to use, say, the set of integers as your universe. That is, you have to express "n is an integer" using a predicate.By the bye, it would help if you could post your proof so that we can see what predicates you might want to choose and such.

 

[Architeuthis Dux]

This means that the problem is asking for a formal representation of the given statement using first-order predicate calculus. This involves defining the domain of all possible values for the variables, which in this case is "anything", and then using logical symbols and quantifiers to express the statement in a precise and unambiguous manner. The solution to this problem would involve using the appropriate logical symbols, quantifiers, and predicates to represent the given statement and prove its validity.