Mathematics
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.
Answer
The negative (additive inverse) of a rational number is obtained by changing its sign.
⇒ -5 + 5 = 0
⇒ 5 + (-5) = 0
So, the negative of -5 is 5 and the negative of 5 is -5, i.e. the Assertion (A) is true.
The Reason (R) states that the negative of a negative rational number is negative, which is wrong, as the negative of a negative rational number is a positive rational number.
So, the Reason (R) is false.
Hence, Option 3 is the correct option.
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,
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.
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.