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Real Numbers

Number of irr...

Question

Number of irrational numbers are greater than the number of rational numbers.

A

True

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B

False

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Solution

The correct option is B False

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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.

State, in each case, whether the given statement is true or false.

(i) The sum of two rational numbers is rational.

(ii) The sum of two irrational numbers is irrational.

(iii) The product of two rational numbers is rational.

(iv) The product of two irrational numbers is irrational.

(v) The sum of a rational number and an irrational number is irrational.

(vi) The product of a nonzero rational number and an irrational number is a rational number.

(vii) Every real number is rational.

(viii) Every real number is either rational or irrational.

(ix) $π$ is irrational and $\frac{22}{7}$ is rational.

Q. Rational and irrational numbers are the two main categories of real numbers.

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. Give an example of each, of two irrational numbers whose:
(i) difference is a rational number.
(ii) difference is an irrational number.
(iii) sum is a rational number.
(iv) sum is an irrational number.
(v) product is an rational number.
(vi) product is an irrational number.
(vii) quotient is a rational number.
(viii) quotient is an irrational number.

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