TMUA Official 2018 Paper 2 · Question 12

Consider the following statement:

For any positive integer $N$ there is a positive integer $K$ such that $N(Km+1)-1$ is not prime for any positive integer $m$ .

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

AFor any positive integer

N

there is a positive integer

K

such that there is a positive integer

m

for which

N(Km+1)-1

is prime.

BFor any positive integer

N

there is a positive integer

K

such that there is a positive integer

m

for which

N(Km+1)-1

is not prime.

CFor any positive integer

N

there is a positive integer

K

such that for any positive integer

m

N(Km+1)-1

is not prime.

DFor any positive integer

N

, any positive integer

K

and any positive integer

m

N(Km+1)-1

is not prime.

EThere is a positive integer

N

such that for any positive integer

K

there is a positive integer

m

for which

N(Km+1)-1

is not prime.

FThere is a positive integer

N

such that for any positive integer

K

there is a positive integer

m

for which

N(Km+1)-1

is prime.

GThere is a positive integer

N

such that for any positive integer

K

and any positive integer

m

N(Km+1)-1

is prime.

HThere is a positive integer

N

and a positive integer

K

for which there is no positive integer

m

for which

N(Km+1)-1

is prime.

examday