Any help with this question would be great, thanks.
Show that if S and T are representable sets of numbers then so are;
S intersection T
S union T
N-S (where N are the natural numbers)
When will you people learn to post relevant details? Logic is a subject notorious for having multiple ways of defining the same concepts.
I assume that a set S is by definition representable when there is a formula F(x) in the language of Peano arithmetic such that for every natural number n, n is in S iff F(n) is true in the standard model (the usual natural numbers).
If this is the case, the answer is trivial: take conjunction, disjunction and negation and the formulas that represent S and T.