Another type of mathematical identity, called a
"property" or a "law," describes how differing variables relate to each
other in a system of numbers. One of these properties is known as the
commutative property, and it applies equally to addition and
multiplication. In essence, the commutative property tells us we can reverse
the order of variables that are either added together or multiplied together
without changing the truth of the expression:
Along with the commutative properties of addition and multiplication, we
have the associative property, again applying equally well to
addition and multiplication. This property tells us we can associate groups
of added or multiplied variables together with parentheses without altering
the truth of the equations.
Lastly, we have the distributive property, illustrating how to
expand a Boolean expression formed by the product of a sum, and in reverse
shows us how terms may be factored out of Boolean sums-of-products:
To summarize, here are the three basic properties: commutative,
associative, and distributive.
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