7. (a) Prove that if m + n and n + p are odd integers, where m, n, and p are integers, then m+p is even. What kind of proof did you use?
(b) Prove that for all integers a, b, n, if n = a + b, then a ≤n/2 or b ≤ n/2 using proof by contradiction.
(c) Prove that if n is any integer, then n² + n is even.
(d) Prove that there are real numbers and y whose sum is 5 and whose product is 6.
(e) Disprove that the sum of two irrational numbers is also an irrational number.
