For each statement below, indicate whether it is true or false, and briefly explain your reasoning in one or two sentences. The symbols "x", " y ", and "z" below refer to attributes, not values. You do not need to give a formal mathematical proof, just give a well-reasoned and complete explanation. You can make up instances as examples or counter-examples to help make your point. Problem 5a) If {x} is a key, then any set containing x is also a key. Problem 5b) If {x} is a superkey, then any set containing x is also a superkey. Problem 5c ) If {x} is a key, then {x} is also a superkey. Problem 5d ) If {x} is a superkey and {y} is a superkey, then {x,y} is a superkey Problem 5e) If {x} is a superkey and {x,y} is a superkey, then {y} is a superkey Problem 5f) If {x,y,z} is a superkey, then one of {x},{y}, or {z} must also be a superkey. Problem 5g ) If a schema consists entirely of {x,y,z}, and if none of the proper subsets of {x,y,z} are keys, then {x,y,z} must be a key. Problem 5h) If the schema for some relation consists entirely of {x,y,z}, and {y} is the key, then the number of unique pairs in the relation is equal to the number of values