Assertion (A): The integer which is 2 less than its additive inverse is -1.
Reason (R): For an integer a, (-a) is its additive inverse.
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 but 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 reason states that for any integer a, its additive inverse is −a.
This is a fundamental definition in mathematics. The sum of an integer and its additive inverse is always zero [a + (−a) = 0].
∴ Reason (R) is true.
Let the unknown integer be x.
According to the Reason (R), its additive inverse is −x.
The assertion states that the integer x is 2 less than its additive inverse. We can write this as an equation:
⇒ x = (−x) − 2
To solve for x, we can add x to both sides of the equation:
⇒ x + x = −2
⇒ 2x = −2
Dividing both sides by 2 gives:
⇒ x = −1
The integer is indeed −1.
∴ Assertion (A) is true.
∴ Both A and R are true and R is the correct explanation of A.
Hence, option 1 is the correct option.
Assertion (A): All whole numbers are integers.
Reason (R): On the number line, all the integers on the left of 0 are 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 but 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
According to Assertion: All whole numbers are integers.
By definition, whole numbers are the set {0, 1, 2, 3, ...}. Integers are the set {..., -3, -2, -1, 0, 1, 2, 3, ...}. Since all whole numbers are included in the set of integers.
∴ Assertion (A) is true.
According to Reason: On the number line, all the integers on the left of 0 are negative.
This is a fundamental property of the number line; numbers to the left of zero are negative, and numbers to the right are positive.
∴ Reason (R) is true.
Both A and R are true but R is not the correct explanation of A.
Hence, option 2 is the correct option.