(Solution by Geneviève Lalonde, Massey, Ontario:)

In this diagram the various regions are numbered. Since all plinks are plonks, there can be nothing in region 1 or 6. And since some plunks are plinks, the regions 6 and 7, considered together, cannot be empty. Combining these conclusions shows that region 7 can’t be empty. Now:

Statement X says that regions 1 and 4 are both empty. We know nothing about region 4, so we can’t say whether this statement is true.

Statement Y says that regions 5 and 7, considered together, can’t be empty. We know that region 7 is not empty, so this statement is true.

Statement Z says that regions 1 and 4, considered together, can’t be empty. We’ve established that region 1 is empty, but again, we know nothing about region 4, so we don’t know whether this statement is true.

Hence the only statement that must be true is Y.