(a) Either prove or give a counterexample: if {u, v} is an edge in an undirected graph, and during depthfirst search post(u) < post(v), then v is an ancestor of u in the DFS tree.

(b) You are given a tree T = (V,E) (in adjacency list format), along with a designated root node r V. Recall that u is said to be an ancestor of v in the rooted tree if the path from r to v in T passes through u. You wish to preprocess the tree so that queries of the form is u an ancestor of v? can be answered in constant time. The preprocessing itself should take linear time. How can this be done?