1. Let A, B, S and T be non-empty subsets of vertices of a DAG G. If A and B are d-separated by S and A and S are d-separated by T, are A and B d-separated by T '? (prove the claim, or provide a counter-example) 2. Let G = (V, E) be a DAG and let G M = (V, EM) be an undirected graph such that we have an edge 1' j in EM when i, j are both parents of the same node in G, or when there is a directed edge 15 > 3' or 3' > i in E (GM is known as the moral graph of G). Let A,B,S be three sets of disjoint vertices. Show that if A and B are separated by S in GM, then they are d-separated by S in G. 3. Consider a v-structure network X )- Z