Write the negation of the statement, for all positive integers n, $n^{2}$ + 41n + 41 is a prime number.

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Solution

There is atleast one positive integer n for which $n^{2}$ + 41n + 41 is not prime.

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Similar questions

Write the negation of each of the following statements in two different ways.

(i) Africa is a continent.

(ii) $\sqrt{5}$ is rational.

(iii) All integers are rational numbers.

(iv) Some prime numbers are odd numbers.

(v) Everyone in Germany speaks German.

n

n^{3} - 8 n^{2} + 20 n - 13

Write the negation of the following compound statement.

'Square of an integer is positive or negative'.

p < q

r < s

p^{2} + q^{2} = r^{2} + s^{2}

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