Prove that the following statement is false. There exists an integer n such that 6n2 + 27 is prime.
To prove the statement is false, prove the negation is true. Write the negation of the statement.
For every integer n, 6n² + 27 is prime.
For every integer n, 6n2 + 27 is not prime.
There exists an integer n, such that 6n2 + 27 is not prime.
There exists a composite number q = 6n2 + 27, such that n is an integer.
There exists an integer n, such that 6n2 + 27 is prime.
Now prove the negation.
Suppose n is any integer. Express 6n2 + 27 as the following product:
6n2 + 2
Now is an integer because sums and products of integers are integers.
Thus, 6n2 + 27 is not prime because it is a of.