(a) Give a proof by contradiction of: for alle R, if r2 is irrational, then I is irrational. (b) Give a proof by contraposition of: for all integers n, if 3n-5 is even, then n is odd. (c) Give a proof by cases of: rsal for all real numbers r. (d) Give a direct proof of: if x and y are odd integers, then + y is even." (e) Prove or disprove: for all real numbers z and y, x-y] = [x]-