Mathematics
Assertion (A): For any rational numbers x, y, z, we have, x × (y + z) = x × y + x × z.
Reason (R): Rational numbers are associative under addition and multiplication.
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.
Rational Numbers
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Answer
For any three rational numbers x, y and z, we have x × (y + z) = x × y + x × z, which is the distributive law of multiplication over addition.
So, the Assertion (A) is true.
Also, for any three rational numbers, (x + y) + z = x + (y + z) and (x × y) × z = x × (y × z), so rational numbers are associative under addition as well as under multiplication.
So, the Reason (R) is also true, but it states the associative law, whereas the Assertion (A) is based on the distributive law.
So, the Reason (R) is not the correct explanation of the Assertion (A).
Hence, Option 2 is the correct option.
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Related Questions
Assertion (A): Rational numbers are closed under addition and multiplication but not under subtraction.
Reason (R): For any two rational numbers a and b,
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