Concept: The sign of a product depends on the signs of the factors. A negative times a positive gives a negative number, which is always less than zero.
Explanation: Check each option:
Option A: For any two integers, a and b, a × (-b) is always negative.
This is false. If a is negative, then a × (-b) becomes positive (negative × negative = positive).
Option B: Difference of two negative integers cannot be positive.
False. Example: (-2) - (-5) = 3, which is positive.
Option C: Product of a negative integer with another negative integer will give an integer smaller than both the integers.
False. Example: (-2) × (-3) = 6. Here 6 is larger than both -2 and -3.
Option D: Product of a negative integer with a positive integer will be an integer less than 0.
True. Example: (-3) × 2 = -6, and -6 < 0. This holds for any such pair.
Answer: Option D: Product of a negative integer with a positive integer will be an integer less than 0.