  For $X = S^2 \times S^2$ and $\mathbb{CP}^2 \# \overline{\mathbb{CP}^2}$, we
show that there exists a link with 2 components which is not smoothly slice in
$X$. By contrast, it is well-known that every knot (i.e., link with 1
component) is smoothly slice in both $S^2 \times S^2$ and $\mathbb{CP}^2 \#
\overline{\mathbb{CP}^2}$. Our proof uses classical topological and smooth
obstructions, as well as constructive arguments to exploit the symmetries of
the problem. As a side note, we also show that for every compact 4-manifold
there exists a link that is not slice in it (either smoothly or topologically).
