Show that the right rotate operation of a red-black tree retains binary search tree properties. You do not need to refer to the algorithm, just to figure 13.2 on page 313. You will show this using inequalities between x, y, , , and .

LEFT-ROTATE x) RIGHT-ROTATE(T, y) Figure 13.2 The rotation operations on a binary search tree. The operation LEFT-ROTATE(T, x) transforms the configuration of the two nodes on the right into the configuration on the left by chang- ing a constant number of pointers. The inverse operation RIGHT-ROTATE(T, y) transforms the con- figuration on the left into the configuration on the right. The letters a B, and y represent arbitrary subtrees. A rotation operation preserves the binary-search-tree property: the keys in a precedex.key which precedes the keys in B, which precede y.key, which precedes the keys in y