Sure, let's identify the addition properties illustrated by each example:
1. [tex]\( A + (B + C) = (A + B) + C \)[/tex] - This is the associative property of addition, as given.
2. [tex]\( A + B = B + A \)[/tex] - This illustrates the commutative property of addition. The commutative property states that the order in which two numbers are added does not affect the sum.
3. [tex]\( A + (-A) = 0 \)[/tex] - This illustrates the additive inverse property. The additive inverse property states that any number plus its inverse (opposite) equals zero.
4. [tex]\( A + 0 = A \)[/tex] - This illustrates the identity property of addition. The identity property of addition states that any number plus zero is that number itself.
So, the addition properties are:
2. [tex]\( A + B = B + A \)[/tex] is the commutative property.
3. [tex]\( A + (-A) = 0 \)[/tex] is the additive inverse property.
4. [tex]\( A + 0 = A \)[/tex] is the identity property.
