Problem 2. [10 points] Prove that if a is an odd integer, then 3a+1 is an even integer. 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 x5 is rational b. [10 points] If x5 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 mn 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