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.

(c) Every real number is always rational.

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

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Solution

(d) Every real number is either rational or irrational.Because a real number can be further categorised into either a rational number or an irrational number, every
real number is either rational or irrational.

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Similar questions

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.

Every Real number is either a Rational number or Irrational Number.

π

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