For what values of \(t\) is the tree of Figure 18.1 a legal B-tree?

By definition (5a, 5b), every non-root node must have at least \(t - 1\) keys and every node may have at most \(2t-1\) keys. The tree in Figure 18.1 has a root node with a single key, and then every other node has 2 or 3 keys. So \(2t-1 \ge 3\) and \(t - 1 \le 2\) which means the minimum degree \(t\) of this tree can be either 2 or 3.