explain cummutative , associate ,closer and additive property
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Associative and Commutative Properties
Grouping Versus Ordering of Elements of Equations in Statistics and Probability
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The associative property concerns itself with the regrouping of elements and an operation. C.K.Taylor
by Courtney Taylor
Updated August 28, 2017
There are several named properties in mathematics that are used in statisticsand probability; two of these types of properties, the associative and commutative properties, are found in the basic arithmetic of the integers, rationals, and real numbers, but also show up in more advanced mathematics.
These properties are very similar and can be easily mixed up, so it is very important to know the difference between the associative and commutative properties of statistical analysis by first determining what each individually represents then comparing their differences.
Commutative property concerns itself with the ordering of certain operations wherein the operation * is commutative of a given set (S) if for every x and y value in the set x * y = y * x. Associative property, on the other hand, is only applied if the grouping of the operation is not important wherein the operation * is associative on the set (S) if and only if for every x, y, and z in S, the equation can read (x * y) * z = x * (y * z).
Defining Commutative Property
Simply put, the commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation. The commutative property, therefore, concerns itself with the ordering of operations including the addition and multiplication of real numbers, integers, and rational numbers and matrix addition.
On the other hand, subtraction, division, and matrix multiplication are not operations that can be commutative because the order of operations is important — for example, 2 - 3 is not the same as 3 - 2, therefore the operation does not a commutative property.
As a result, another way to express the commutative property is through the equation ab = ba wherein no matter the order of the values, the results will always be the same.
Associative Property
The associative property of an operation exhibits associativity if the grouping of the operation is not important, which can be expressed as a + (b + c) = (a + b) + c because no matter which pair is added first because of the parenthesis, the result will be the same.
Associative and Commutative Properties
Grouping Versus Ordering of Elements of Equations in Statistics and Probability
Share

The associative property concerns itself with the regrouping of elements and an operation. C.K.Taylor
by Courtney Taylor
Updated August 28, 2017
There are several named properties in mathematics that are used in statisticsand probability; two of these types of properties, the associative and commutative properties, are found in the basic arithmetic of the integers, rationals, and real numbers, but also show up in more advanced mathematics.
These properties are very similar and can be easily mixed up, so it is very important to know the difference between the associative and commutative properties of statistical analysis by first determining what each individually represents then comparing their differences.
Commutative property concerns itself with the ordering of certain operations wherein the operation * is commutative of a given set (S) if for every x and y value in the set x * y = y * x. Associative property, on the other hand, is only applied if the grouping of the operation is not important wherein the operation * is associative on the set (S) if and only if for every x, y, and z in S, the equation can read (x * y) * z = x * (y * z).
Defining Commutative Property
Simply put, the commutative property states that the factors in an equation can be rearranged freely without affecting the outcome of the equation. The commutative property, therefore, concerns itself with the ordering of operations including the addition and multiplication of real numbers, integers, and rational numbers and matrix addition.
On the other hand, subtraction, division, and matrix multiplication are not operations that can be commutative because the order of operations is important — for example, 2 - 3 is not the same as 3 - 2, therefore the operation does not a commutative property.
As a result, another way to express the commutative property is through the equation ab = ba wherein no matter the order of the values, the results will always be the same.
Associative Property
The associative property of an operation exhibits associativity if the grouping of the operation is not important, which can be expressed as a + (b + c) = (a + b) + c because no matter which pair is added first because of the parenthesis, the result will be the same.
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