Which one of the following is/are correct?
(A) Every irrational number is a real number.
(B) Every real number is an irrational number.
(C) The sum or difference of a rational number and an irrational number is an irrational number.
(D) The product or quotient of a non-zero rational number with an irrational number is an irrational number.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (C) and (D) only
Statement (A): Every irrational number is a real number. Correct. All irrational numbers belong to the set of real numbers, along with rational numbers.
Statement (B): Every real number is an irrational number. Incorrect. Real numbers include both rational and irrational numbers, so not every real number is irrational.
Statement (C): The sum or difference of a rational number and an irrational number is an irrational number. Correct. Adding or subtracting a rational number from an irrational number always results in an irrational number.
Statement (D): The product or quotient of a non-zero rational number with an irrational number is an irrational number. Correct. Multiplying or dividing an irrational number by a non-zero rational number gives an irrational result.