1. The problem statement, all variables and given/known data Disprove: There is a positive integer n such that n2+3n+2 is prime. 2. Relevant equations Disprove existential statements by proving that the negation is true. 3. The attempt at a solution So my book goes over how to disprove this by proving the negation is true: For all positive integer n, n2+3n+2 is composite. n2+3n+2 = (n+1)(n+2) which must be composite, because n>1, so the original statement is false. Isn't proving that the negation true useless in this situation? Wouldn't proving the original false also be valid? For example: n2+3n+2 = (n+1)(n+2) (n+1) and (n+2) will always be greater than 1, so there doesn't exist an integer n such that n2+3n+2 is prime.