tmua.me Medium Set A Paper 2 · Question 14

A function $f$ assigns a real number to each positive integer. Consider the statement:

For every positive real number $a$ , there is a positive integer $n$ such that $f(n)>a$ and $f(n+1)>a$ .

Which of the following is the negation of this statement?

AThere is a positive real number

a

such that, for every positive integer

n

, both

f(n)\leq a

and

f(n+1)\leq a

BFor every positive real number

a

, there is a positive integer

n

such that

f(n)\leq a

f(n+1)\leq a

CThere is a positive integer

n

such that, for every positive real number

a

f(n)\leq a

f(n+1)\leq a

DFor every positive integer

n

, there is a positive real number

a

such that

f(n)\leq a

and

f(n+1)\leq a

EThere is a positive real number

a

such that, for every positive integer

n

f(n)\leq a

f(n+1)\leq a

examday