There are two statements, namely, Assertion (A) and Reason (R) given below. Choose the correct option in context of the statements.

Assertion(A): $3$ is an irrational number.

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

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

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

Assertion (A) is true and Reason (R) is false.

Assertion (A) is false and Reason (R) is true.

answer is B.

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Detailed Solution

Here, we are given the assertion as follows:

3

is an irrational number.
The value of

3

1.732050808.....

.
It can be observed that the decimal obtained as a square root is neither terminating nor repeating.
Thus, by definition,

3

is an irrational number as it can never be expressed as a fraction.
Therefore, the given assertion is true.
Next, the reason for the assertion statement is given as the sum of a rational and irrational number is an irrational number.
This is also a true statement but, it does not have to do anything with

3

being a rational number.
So, we can conclude that both the assertion and the reason are true, but the reason is not the correct explanation of the assertion. Hence, the correct option is (2).

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