  Jel\'inek, Mansour, and Shattuck studied Wilf-equivalence among pairs of
patterns of the form $\{\sigma,\tau\}$ where $\sigma$ is a set partition of
size $3$ with at least two blocks. They obtained an upper bound for the number
of Wilf-equivalence classes for such pairs. We show that their upper bound is
the exact number of equivalence classes, thus solving a problem posed by them.
