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.
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 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, , which is a rational number.
So, the Assertion (A) is false.
Hence, Option 4 is the correct option.
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Related Questions
Fill in the blanks:
(i) depicts ……… property of addition of rational numbers.
(ii) The multiplicative inverse of a rational number is also called its ………
(iii) The multiplicative inverse of a negative rational number is a ……… rational number.
(iv) The numbers ……… and ……… are their own reciprocals.
(v) ……… = 1
(vi) ……… = 1
(vii) Among the greatest rational number is ………
Write true (T) or false (F):
(i) Every rational number has a reciprocal.
(ii) Subtraction of rational numbers is commutative.
(iii) The additive inverse of is -4.
(iv) is a rational number.
(v) 0 is the smallest rational number.
(vi) The multiplicative inverse of is .
(vii) There are countless rational numbers between .
Assertion (A): The negative (additive inverse) of -5 is 5 and the negative of 5 is -5.
Reason (R): The negative of a negative rational number is negative and the negative of a positive rational number is negative.
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.
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.