Question

Which one of the following statements is correct?
A. There can be a real number which is both rational and irrational.
B. The sum of two irrational numbers is rational.
C. Every integer is a rational number.
D. None of these

Answer 1

Hint: We will be using the concepts of the number system to solve the problem. We will be using the concepts of rational number, irrational number and integer to solve the problem. We will check each option to find the correct answer.

Complete step-by-step answer:
Now, we have in option (A) that there can be a real number which is both rational and irrational but this is not true since rational and irrational numbers are disjoint sets of real numbers.
Now, in option (B) we have that the sum of two irrational numbers is rational. This is also not correct as if we have $\sqrt{2},\sqrt{3}\ then\ \sqrt{2}+\sqrt{3}$ is also an irrational number. So, this statement is not correct for all irrational numbers.
Now, in option (C) we have that every integer is a rational number, which is true because integers are subsets of rational numbers. Also we can represent any integer \[x\in \mathcal{Z}\ as\ \dfrac{x}{1}\] where x and 1 are co primes and $1\ne 0$. So, the correct option is (C).

Note: To solve these types of questions it is important to know the different types of classification of numbers like rational, irrational, integer, etc. Also the relation between them like every integer is a rational number.