Mark the following statements as True or False.

Every real number is a rational number.

There are numbers that are not real.

Some rational numbers can be irrational numbers

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Solution

A. Real number is a set of both rational as well as irrational numbers. Hence, the first statement is false.

B. There are numbers that do not fall under the category of real numbers. They are called complex numbers, but they are out of scope for this chapter. : True

C. Rational numbers can never be irrational. Numbers are either rational, or they aren't. They cannot be both rational and irrational. : False

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Similar questions

Find whether the following statements are true or false :

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

(ii) $π$ is an irrational number.

(iii) Irrational numbers cannot be represented by points on the number line.

Which of the following is a true statement ?

(a) The sum of two irrational numbers is an irrational number.

(b) The product of two irrational numbers is an irrational number.

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

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.

State, in each case, whether true or false.

$(i) \sqrt{2} + \sqrt{3} = \sqrt{5}$

$(i i) 2 \sqrt{4} + 2 = 6$

$(i i i) 3 \sqrt{7} - 2 \sqrt{7} = \sqrt{7}$

$(i v) \frac{2}{7}$ is an irrational number.

$(v) \frac{5}{11}$ is a rational number.

(vi) All rational numbers are real numbers.

(vii) All real numbers are rational numbers.

(viii) Some real numbers are rational numbers.

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Every real number is a rational number.
There are numbers that are not real.
Some rational numbers can be irrational numbers