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The COMMUTATIVE property states that the order of the arguments of an operation does not matter. In symbolic terms, for elements a and b and for the operation ~, a ~ b = b ~ a

The ASSOCIATIVE property states that the order in which the operation is carried out does not matter. Symbolically, for elements a, b and c, (a ~ b) ~ c = a ~ (b ~ c) and so, without ambiguity, either can be written as a ~ b ~ c.

The DISTRIBUTIVE property is a property of two operations, for example, of multiplication over addition. It is not the property of a single operation. For operations ~ and # and elements a, b and c, symbolically, this means that a ~ (b # c) = a ~ b # a ~ c.

The existence of an IDENTITY is a property of the set over which the operation ~ is defined; not a property of operation itself. Symbolically, if the identity exists, it is a unique element, denoted by i, such that a ~ i = a = i ~ a for all a in the set.

For example, you can define addition on all positive integers which will have the commutative and associative properties but the identity (zero) and additive inverses (negative numbers) are undefined as far as the set is concerned.

I have deliberately chosen ~ and # to represent the operations rather than addition or multiplication because there are circumstances in which these properties do not apply to multiplication (for example for matrices), and there are many other operations that they can apply to.

Q: What is the distributive property the commutative property the associate property and the identity property?

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These are characteristics of the elements of algebraic structures, or algebraic sets. Each element in the set possesses these characteristics and that is why they are called properties.

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.A + B = B + C Commutative property(A+B) + C = A + (B +C) Associative PropertyA + 0 = A Additive Identity PropertyA*(B + C) = A*B + A*C Distributive property

They are the associative property, distributive property and the commutative property.

no; commutative

identity property

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distributive

Which property is illustrated in this problem? (associative, distributive, identity, or commutative) 7d + 3 = 3 + 7d

These are characteristics of the elements of algebraic structures, or algebraic sets. Each element in the set possesses these characteristics and that is why they are called properties.

distributive, associative, commutative, and identity (also called the zero property)

The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.

There are four mathematical properties which involve addition. The properties are the commutative, associative, additive identity and distributive properties.A + B = B + C Commutative property(A+B) + C = A + (B +C) Associative PropertyA + 0 = A Additive Identity PropertyA*(B + C) = A*B + A*C Distributive property

They are the associative property, distributive property and the commutative property.

no; commutative

Commutative: a × b = b × a Associative: (a × b) × c = a × (b × c) Distributive: a × (b + c) = a × b + a × c

according to commutative property both the distributive laws are equal why to use two distributive laws

It is the commutative property of multiplication.

These are properties of algebraic structures with binary operations such as addition and/or subtraction defined on the set.The identity property, refers to a unique element of the set with special properties with respect to an operation.The commutative property states that the order of the operands does not matter. There are many algebraic structures where this property does not hold. The set of numbers with the operation subtraction or division do not have this property.The associative property states that the order in which a repeated operation is carried out does not matter.The distributive property is applicable when there are two binary operations defined on the set.