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Problem 3. [30 points] Recall that a rational number can be put in the form qp where p and q ...
Problem 3. [30 points] Recall that a rational number can be put in the form qp? where p and q are integers and q?=0. Prove the following for any rational number, x : a. [10 points] If x is rational, then x?5 is rational b. [ 10 points] If x?5 is rational, then x/3 is rational c. [ 10 points] If x/3 is rational, then x is rational Problem 4. [20 points] Consider the statement: For all integers m and n, if m?n is odd, then m is odd or n is odd. a. [10 points] Prove the statement using a proof by contrapositive b. [10 points] Prove the statement using a proof by contradiction