If x and y are negative integers, then which of the following statements is/are always true?
(A) x + y is positive integer.
(B) xy is positive integer.
(C) x - y is positive integer.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → (B) only
“Always true” means true for every pair of negative integers; one pair that fails is enough to reject a statement.
(A) x + y is positive integer. Incorrect. Adding two negative numbers gives a number further below zero: \((-2)+(-3)=-5\). The sum is always negative.
(B) xy is positive integer. Correct. The product of two negative numbers is always positive: \((-2)\times(-3)=6\).
(C) x - y is positive integer. Incorrect. The sign of \(x-y\) depends on which number is larger: \(x=-2, y=-5\) gives \(-2-(-5)=3\), but \(x=-5, y=-2\) gives \(-5-(-2)=-3\), and \(x=y\) gives 0.