TMUA Viluxent Set 1 Paper 2 · Question 13

Consider the statement:

“For every real number $x$ , there exists a real number $y$ such that $x+y>5$ and $xy<1$ .”

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

AThere exists a real number

x

such that, for every real number

y

x+y\le5

and

xy\ge1

BFor every real number

x

, there exists a real number

y

such that

x+y\le5

xy\ge1

CThere exists a real number

x

such that, for every real number

y

x+y\le5

xy\ge1

DThere exists a real number

x

such that, for every real number

y

x+y\le5

xy\ge1

, and there exists such a

y

EFor every real number

x

, for every real number

y

x+y\le5

xy\ge1

FThere exists a real number

x

such that, for every real number

y

x+y<5

xy>1

examday