Question

Which of the following statements is not true?

• A. When two positive integers are added, we always get a positive integer.
• B. When two negative integers are added we always get a negative integer.
• C. When a positive integer and a negative integer are added we always get a negative integer.
• D. The additive inverse of an integer $2$ is $(-2)$ and the additive inverse of $(-2)$ is $2$.

Answer 1

The correct option is C

When a positive integer and a negative integer are added we always get a negative integer.

Step 1. Explanation for correct option.

Option (C): When a positive integer and a negative integer are added we always get a negative integer.

When a positive and a negative integer are added, the result is always a negative integer.

For example: Consider a positive integer $7$ and a negative integer $-5$ then their sum is $7+(-5)=2$, which is a positive number.

Hence, the correct answer is “Option C”.

Step 2. Explanation for incorrect options.

Option (A): When two positive integers are added, we always get a positive integer.

For example : Consider two positive integers $2$ and $3$ then their sum is $2+3=5$ which is a positive integer.

Option (B): When two negative integers are added we always get a negative integer.

For example : Consider two negative integers $-2$ and $-3$ then their sum is $-2+\left(-3\right)=-5$ which is a negative integer.

Option (D): The additive inverse of an integer $2$ is $(-2)$ and the additive inverse of $(-2)$ is $2$.

The additive inverse of any integer $a$ is $-a$.

So, the additive inverse of an integer $2$ is $-2$.

Hence, Statements in “Option A, Option B, and Option D” are true.

Hence, the correct answer is “Option C”.