Daniel J Smith Custom TMUA Set A Paper 2 · Question 8

Consider the statement:

For every positive integer $n$ there exists a positive integer $k$ such that for all positive integers $m$ , the number $n(m+k)$ is not a square

Which one of the following is the negation of this statement?

AFor every positive integer

n

there exists a positive integer

k

such that for every positive integer

m

, the number

n(m+k)

is a square.

BThere exists a positive integer

n

such that for every positive integer

k

and every positive integer

m

, the number

n(m+k)

is not a square.

CThere exists a positive integer

n

such that there exists a positive integer

k

for which

n(m+k)

is a square for all positive integers

m

DFor every positive integer

n

, for every positive integer

k

, there exists a positive integer

m

such that

n(m+k)

is not a square.

EThere exists a positive integer

n

such that for every positive integer

k

there exists a positive integer

m

such that

n(m+k)

is a square.

examday