A rational number is a number that can be expressed in the form ab where a and b are integers and b is not 0. An irrational number is a number that cannot be expressed in the form ab for any integers a and b. Prove or disprove the following: (a) 7 is an irrational number. (b) The product of two irrational numbers is irrational. (c) The sum of two irrational numbers is irrational. (d) If a is a rational number then its inverse 1 a is a rational number. (e) If a is an irrational number then its inverse 1 a is an irrational number.

Given a positive integer n prove the following: n is even if and only if 13n + 8 is even.