# Get Answers to all your Questions

#### Let S be a non-empty subset of R. Consider the following statement:P : There is a rational number such that Which of the following statements is the negation of the statement P ? Option 1) There is a rational number such that .    Option 2) There is no rational number such that . Option 3) Every rational number satisfies  . Option 4) and is not rational.

As we learnt in

Negation of a Statement -

Symbol of negation is

- wherein

We write it up as p

There is rational numbers    such that

negation is every rational number   satisfies

Since negation of is

Option 1)

There is a rational number such that .

Incorrect option

Option 2)

There is no rational number such that .

Incorrect option

Option 3)

Every rational number satisfies  .

Correct option

Option 4)

and is not rational.

Incorrect option