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Mathematics

Assertion: Difference of two negative integers cannot be a positive integer.

Reason: For any two integers a and b, a - b = a + (additive inverse of b)

  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 but 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.

Integers

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Answer

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

Explanation

The assertion is false because the difference of two negative integers can be positive.

Example:

(-3) - (-7) = -3 + 7 = 4
which is positive.

The reason is true because subtraction of integers is defined as adding the additive inverse:

a - b = a + (-b)

Hence, option 4 is the correct option.

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