How Is Predicate Calculus Used to Formalize Mathematical Statements?

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The discussion focuses on translating mathematical statements into first-order predicate calculus (FOPC), specifically regarding the proof that a positive integer n is even if and only if 7n + 4 is even. Participants clarify that the Universe of Discourse is "anything," meaning the predicates must be defined without restricting to integers. The initial statement to express in FOPC is that "n is a positive integer." Contributors suggest sharing the proof to better identify suitable predicates for the translation. Understanding these elements is crucial for formalizing the mathematical statements correctly.
majeedh
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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)
 
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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.
 
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