Solution
= Solution
Because the generating sets are disjoint, the <free product> has the presentation
$$
\boxed{G*H=\langle X\sqcup Y\mid R\sqcup S\rangle.}
$$
This is immediate from the <universal property of a group presentation>: a map out of this presented group is exactly a pair of homomorphisms from $G$ and $H$ to the target group.