Please solve this - Thank you :D

4. Determine whether the statement is true or false. Prove the statement directly from the definitions if it is true, and give a counterexample if it is false. (a) The sum of any three consecutive integers is divisible by 3. (b) The product of any two even integers is a multiple of 4. (c) For all integers a, b, and c, if alb and ac then a|(26 3c). (d) For all integers a, b, and c, if abc then a c and bc. (e) For all integers a, b, and c, if a|(b + c) then ab or alc. 5. Prove each of the following statements by contradiction. In addition, for (e) and (f), please also prove them by contraposition. (a) For all odd integers a and b, 62 - - a + 4. (b) For all prime numbers a, b, and c, a + b2 + c2. (c) If a and b are rational numbers, 6 + 0, and r is an irrational number, then a + br is irrational. (d) For any integer n, n2 2 is not divisible by 4. (e) The negative of any irrational number is irrational. (f) For every integer n, if n2 is odd then n is odd