Mathematics, 01.03.2021 22:20, Damagingawsomeness2
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.
Answers: 1
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Prove that the following statement is false.
There exists an integer n such that 6n2 + 27 is prime....
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