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Negation

Are the follo...

Question

Are the following pairs of statements are negation of each other
(i)The number x is not a rational number.
The number x is not an irrational number.

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Solution

The negation of the first statement is the number $x$ is a rational number.
This is same as the second statement. This is if a because if a number is not an irrational number then it is a rational number.

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Q. Are the following pairs of statements are negation of each other:
(i) The number x is not a rational number.
The number x is not an irrational number.
(ii) The number x is not a rational number.
The number x is an irrational number.

Q. Are the following pairs of statements negations of each other?
(i) The number

x

is not a rational number
The number

x

is not an irrational number
(ii) The number

x

is a rational number
The number

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is an irrational number

Find the negation of the statement - 'There exists a rational number x such that its square is 2 '.

Q. Which of the following statements is/are correct?
Statement I: The sum of a rational number and an irrational number is an irrational number.
Statement II: Negative of an irrational number is a rational number.
Statement III: The product of a non-zero rational number and an irrational number is an irrational number.

S

be a non-empty subset of

R

. Consider the following statement :

P :

There is a rational number

x \in S

x > 0

.
Which of the following statements is the negation of the statement

P

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