Let the statement: Consider the following suppositions: (…
Let the statement: Consider the following suppositions: (1) Suppose is any real number such that is rational. (2) Suppose is any real number such that is irrational. (3) Suppose is any irrational number. (4) Suppose is any rational number. (5) Suppose there exists a real number such that is rational and is irrational. (6) Suppose there exists a real number such that is irrational and is rational. (7) Suppose there exists a real number such that and are both irrational. Which should be a correct supposition to begin the proof if we wish to prove using the indicated proof method? (a) Using direct proof. (b) Using proof by contrapositive. (c) Using proof by contradiction.