Jelínek, Mansour, and Shattuck studied Wilf-equivalence among pairs of patterns of the form $\{σ,τ\}$ where $σ$ 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.