Wuu , then a 0. 6. Complete the following proofs: a) Show that if x is irrational then x is irrational, b) Show that if x is irrational and x > 0, then x is irrational. (The real number r is rational if there exist integers p and q with q = 0 such that r = p/q. A real number that is not rational is called irrational.) c) Prove that the following four statements about the integer n are equivalent: i. na is odd; ii. 1-n is even; iii. n is odd; iv. n + 1 is even. d) Prove or disprove the following: Every positive integer can be written as the sum of the squares of three integers. e) Prove that m2 = n2 if and only if m= n or m = -n. f) Show that these statements are equivalent, where a and b are real numbers: i. a is less than b; ii. The average of a and b is greater than a; iii. The average of a and b is less than b. g) Prove that if n is a perfect square, then +2 is not a perfect square. (An integer n is a perfect square if there is an integer k such that n = k.)