Which of the following statements is not true?
When two positive integers are added, we always get a positive integer.
When two negative integers are added we always get a negative integer.
When a positive integer and a negative integer is added we always get a negative integer.
Additive inverse of an integer 2 is (–2) and additive inverse of (–2) is 2.
Why option (c) is NOT true
We will check each option with simple examples.
(a) Two positive integers added → positive
(3 + 5 = 8)
Both numbers are positive, so the sum is also positive.
(b) Two negative integers added → negative
((-2) + (-7) = -(2 + 7))
(= -9)
Adding negatives keeps it negative.
(c) A positive + a negative is always negative ❌
This is not always true. It depends on which number has the bigger size (magnitude).
Case 1: Positive is bigger → sum is positive
(7 + (-2) = 5)
Case 2: Negative is bigger → sum is negative
(2 + (-7) = -5)
Case 3: Equal size → sum is zero
(4 + (-4) = 0)
So it is not “always negative”.
(d) Additive inverse
The additive inverse of a number is what you add to get zero.
(2 + (-2) = 0)
((-2) + 2 = 0)
So the additive inverse of (2) is (-2), and of (-2) is (2).
Correct choice: (c)