Question

Which of the following is the additive inverse of the set of negative integers ?

• A. $0$
• B. Set of negative integers
• C. Set of natural numbers
• D. None of the above

Answer 1

The correct option is C Set of natural numbers

Additive Inverse:

• An additive inverse of a number is defined as the value, which on adding with the original number results in zero.
• It is a value we add to a number to yield zero.
• Suppose, $\ast$ is the original number, then its additive inverse would be minus of $\ast$ i.e.,$-\ast$, such that; $\ast +(-\ast )=0.$

$\underset{–}{\text{Need to find:}}$ Additive inverse of negative integers

Set of negative integers $=\text{{}-1,-2,-3,...\text{}}$

$\therefore$ Additive inverse of negative integers $=\text{{}1,2,\mathrm{3...}\text{}}=$ Set of natural numbers
$(\because -1+\underset{–}{1}=0;-2+\underset{–}{2}=0;...)$

Therefore, the additive inverse of the set of negative integers is the set of Natural Numbers.

$\therefore$ Option (c.) is the correct choice.