1. (9 points) For each of the following, determine whether it is true or false and then prove it (if it is true) or disprove it (if it is false). (a) n2-n+ 41 is prime for every non-negative integer As a reminder, the definition for prime numbers is on page 257. (b) The ratio (result of division) of any two positive rational numbers is rational. As a reminder, the definition for rational numbers is on page 85. (c) The sum of any two irrational numbers is irrational. As a reminder, an irrational number is a real number that is not rational