Statement-1 (Assertion): There are two rational numbers whose sum and product both are rationals. Statement-2 (Reason): There are numbers which cannot be written in the form p/q, q≠0 , p, q both are integers.

Assertion Reason MCQ on Rational Numbers

Question

Statement-1 (Assertion): There are two rational numbers whose sum and product both are rationals.

Statement-2 (Reason): There are numbers which cannot be written in the form \( \frac{p}{q} \), \( q \neq 0 \), where \( p, q \) are integers.

Options:

(a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.

(b) Statement-1 is true, Statement-2 is true; Statement-2 is not a correct explanation for Statement-1.

(d) Statement-1 is false, Statement-2 is true.

Take two rational numbers, for example:

\[ 2 \text{ and } 3 \]

Their sum:

\[ 2 + 3 = 5 \quad (\text{rational}) \]

Their product:

\[ 2 \times 3 = 6 \quad (\text{rational}) \]

So, Statement-1 is true.

Statement-2 is also true because irrational numbers exist (they cannot be written as \( \frac{p}{q} \)).

However, Statement-2 does not explain Statement-1.

✔ Correct option: (b)

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