Question

Assertion: `sqrt(2)` is an irrational number.

Reason: The sum of a rational and an irrational number is irrational.

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

• Assertion (A) is true but Reason (R) is false.

• Assertion (A) is false but Reason (R) is true.

Answer 1

Both Assertion (A) and Reason (R) are true and Reason (R) is not the correct explanation of Assertion (A).

Explanation:

Assertion: `sqrt(2)` is an irrational number. This is true because `sqrt(2)` cannot be expressed as a fraction of two integers.

Reason: The sum of a rational and an irrational number is irrational. This is also true.

However, the reason given is not the correct explanation for why `sqrt(2)` is irrational. The irrationality of `sqrt(2)` is proven differently, not simply because of the sum property stated in the reason.

Therefore, both are true, but the Reason does not correctly explain the Assertion.