Elements of a Subset, Pairwise Relatively Prime!

For every integer \(n > 3\), let \(f(n)\) be the minimum positive integer, such that every subset of the set \(A =\{ 1,2,3,\ldots,n\} \), which contains \(f(n)\) elements, has three elements \(x,y,z\) belonging to \(A\), which are pairwise relatively prime.

Find the value of \(f(1250)\).

Bonus: Generalize for \(f(n)\).

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