tmua.me Medium Set D Paper 2 · Question 14

A nonempty collection $C$ consists of functions from the real numbers to the real numbers. Consider the statement:

For every function $f$ in $C$ , there exist real numbers $x<y$ such that $f(x)\geq0$ and $f(y)<0$ .

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

AThere is a function

f

C

such that, for every pair of real numbers

x<y

, both

f(x)<0

and

f(y)\geq0

BFor every function

f

C

, there exist real numbers

x<y

such that

f(x)<0

f(y)\geq0

CThere exist real numbers

x<y

such that, for every function

f

C

f(x)<0

f(y)\geq0

DThere is a function

f

C

such that, for every pair of real numbers

x<y

f(x)<0

f(y)\geq0

EThere is a function

f

C

such that, for every pair of real numbers

x<y

f(x)\leq0

f(y)>0

examday