The inverse property of addition is an important concept in mathematics. It states that for any number [tex]\( y \)[/tex], there exists another number, called the additive inverse (denoted as [tex]\(-y\)[/tex]), such that when you add these two numbers together, the result is zero.
Let's look at each option and determine which one demonstrates this property:
1. [tex]\( y = y \)[/tex]
This statement simply asserts that any number is equal to itself, which is an example of the identity property, but it does not involve the additive inverse.
2. [tex]\( y + y = 2y \)[/tex]
This statement shows that adding a number to itself results in doubling the number. While true, it does not involve adding the number to its additive inverse.
3. [tex]\( y + (-y) = 0 \)[/tex]
This statement matches the definition of the inverse property of addition. It shows that any number [tex]\( y \)[/tex], when added to its additive inverse [tex]\(-y\)[/tex], results in zero.
4. [tex]\( y + 0 = y \)[/tex]
This statement illustrates the identity property of addition, where any number added to zero results in the number itself. This is not the inverse property.
Among these options, the third statement [tex]\( y + (-y) = 0 \)[/tex] demonstrates the inverse property of addition.
Therefore, the correct statement that shows the inverse property of addition is:
[tex]\[ y + (-y) = 0 \][/tex]
This corresponds to option 3.
