Exercise 2.4.4: Showing a statement is true or false by direct proof or counterexample. About Determine whether the statement is true or false. If the statement is true, give a proof. If the statement is false, give a counterexample. (a) If and are even integers, then is an even integer. Solution (b) If is an even integer, then and are both even integers. (c) If , then . Solution (d) If x and y are real numbers and , then . Solution (e) If and are positive real numbers and , then . (f) The average of two odd numbers is an odd integer. (g) The average of two even numbers is even. (h) The average of two odd numbers is an integer. Solution