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Suppose we have a neighborhood of n houses. For any two houses we pick, there is a road between them. (a) The landlord wants to cut maintenance costs by removing some of the roads. Let k be the minimum number of roads he can remove such that the neighborhood is still connected (every house can be walked to from every other house) and there are no cycles. Determine the value of k as an expression in terms of n. Then indicate how to remove the minimum number of roads from the neighborhood such that the requirements are satisfied. (b) Suppose now instead that the landlord wants to remove houses. Let be the minimum number of houses that must be removed such that the neighborhood is still connected and has no cycles. Removing a house also removes the roads it is connected to. Determine the value of as an expression in terms of n. Then indicate how to remove the minimum number of houses from the neighborhood such that the requirements are satisfied