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 ?
There is a rational number such that .
There is no rational number such that .
Every rational number satisfies .
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
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