Assertion (A): All surds are irrational numbers. Reason (R): All irrational numbers are surds. 1. Assertion (A) is true, Reason (R) is false. 2. Assertion (A) is false, Reason (R) is true. 3. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A). 4. Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

A surd is a number that cannot be expressed as a simple fraction and is the root of a rational number (like ). These roots are always irrational. ∴ Assertion (A) is true. While all surds are irrational, not all irrational numbers are surds. For example, pi (π) is irrational number but are not roots of rational numbers and therefore are not surds. ∴ Reason (R) is false. ∴ Assertion (A) is true, Reason (R) is false. Hence, option 1 is the correct option.

Mathematics

Assertion (A): All surds are irrational numbers.
Reason (R): All irrational numbers are surds.
Assertion (A) is true, Reason (R) is false.
Assertion (A) is false, Reason (R) is true.
Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct reason for Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct reason (or explanation) for Assertion (A).

Rational Numbers

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Rational Numbers

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