Question

how will I identify which axiom to be used for a question​

Answer 1

Answer:

Step-by-step explanation:

I think that the guiding principle is that if you can write a finite specification for what you want to choose then you don't need to rely on AC. To pick a real number, you write a specification

{x∈R:x=2.745}, or whatever.

If you want to pick elements from a finite collection of infinite sets you can compose a finite number of clauses to do so.

If you have an infinite number of choices to make then you might have a common way to make the choice (e.g. take the first element from each set in an infinite collection of ordered sets, the left from each pair in an infinite collection of shoes) which allows you to write a finite specification.

Otherwise, you can rely on AC to say that a set can be formed comprising one element from each set in a (infinite) collection.