Exercise 2.2.2: Showing a statement is true or false by direct proof or counterexample. Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (Note: the definition of an even integer is an integer that can be expressed as 2k, where k is an integer.) (a) If x and y are both even integers, then x+y is an even integer.