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Mathematics

Assertion (A): Rational numbers are closed under addition and multiplication but not under subtraction.

Reason (R): For any two rational numbers a and b,

a + b is a rational number

a - b is a rational number

a × b is a rational number.

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

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

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

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

Rational Numbers

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Answer

For any two rational numbers a and b, each of a + b, a - b and a × b is again a rational number, so rational numbers are closed under addition, subtraction and multiplication.

So, the Reason (R) is true.

But the Assertion (A) claims that rational numbers are not closed under subtraction, which is wrong. For example, 23−14=512\dfrac{2}{3} - \dfrac{1}{4} = \dfrac{5}{12}, which is a rational number.

So, the Assertion (A) is false.

Hence, Option 4 is the correct option.

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