tmua.me Medium Set F Paper 2 · Question 12

A function $f$ is defined for every real number. Consider the statement:

For every real number $k>0$ , there exist distinct real numbers $x$ and $y$ such that $f(x)=f(y)=k$ and $x+y<0$ .

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

AFor every

k>0

, every pair of distinct real numbers

x,y

satisfying

f(x)=f(y)=k

has

x+y\geq0

BThere exist

k>0

and distinct real numbers

x,y

such that

f(x)=f(y)=k

and

x+y\geq0

CThere exists

k>0

such that every pair of distinct real numbers

x,y

satisfying

f(x)=f(y)=k

has

x+y>0

DThere exists

k>0

such that, for every pair of distinct real numbers

x,y

, either

f(x)\ne k

f(y)\ne k

x+y\geq0

EThere exist distinct real numbers

x,y

such that, for every

k>0

, either

f(x)\ne k

f(y)\ne k

x+y\geq0

examday