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 not prime. For every integer n, 6n + 27 is prime. There exists an integer n, such that 6n + 27 is not prime. There exists an integer n, such that 6n + 27 is prime. There exists a composite number q = 6n2 + 27, such that n is an integer. Now prove the negation. Suppose n is any integer. Express 6n2 + 27 as the following product: 6n2 + 27 = 3 Now is an integer because sums and products of integers are integers. Thus, 6n2 + 27 is not prime because it is a ---Select--- of---Select---

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