You should write out all proofs in this homework using complete sentences. You may use symbols in your proof as long as they are still contained within full sentences. Proofs will be graded on both content and presentation. You may assume that the product, sum, and difference of any two integers is an integer. 1. We will say that a number is a square root integer if it has the form a + E's/i where o and b are integers. a) Prove that the square root integers are closed under addition. b} Prove that the square root integers are closed under multiplication. 2. Determine whether the following statements are true or false. If the statement is true, provide a proof. a} The sum of any two odd numbers is an odd number. b} The sum of any two odd numbers is an even number