Decide whether the statements below about subgraphs are true or false. For those that are true, briefly explain why (1 or 2 sentences). For any that are false, give a counterexample.
Any subgraph of a complete graph is also complete.
Any induced subgraph of a complete graph is also complete.
Any subgraph of a bipartite graph is bipartite.
Any subgraph of a tree is a tree.