How to denote the first or the second part of a Cartesian product?

Question

I have a set of the form $$S:=\{(a_1,b_1),(a_2,b_2),\ldots,(a_n,b_n)\}.$$

Is there a notation for the first (or second) part of $S$ without defining them?

In fact, I can say let $A:=\{a_1,a_2\ldots,a_n\}$ and $B:=\{b_1,b_2\ldots,b_n\}$ but here I am defining them. Is there a notation like $S(1)$ to denote $A$ or $S(2)$ to denote $B$?