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Commutative law: The order of the operands doesn't change the result. For example, 4 + 3 = 3 + 4.
Associative: (1 + 2) + 3 = 1 + (2 + 3) - it doesn't matter which addition you do first.
Both laws are valid for addition, and for multiplication (as these are usually defined, with numbers. However, special "multiplications" have been defined that are not associative, or not commutative - for example, the cross product of vectors, or multiplication of matrices are not commutative.
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An example of binary operation which is commutative but not associative?
NAND
Do the commutative and associative laws apply to vector subtraction?
No, changing order of vectors in subtraction give different resultant so commutative and associative laws do not apply to vector subtraction.
How are commutative and associative properties the same?
the switch the numbers arond
How you do Multiplication property?
The multiplication properties are: Commutative property. Associative property. Distributive property. Identity property. And the Zero property of Multiplication.
What is associative property of addition?
The associative property of addition means that the order in which you add terms doesn't matter.(1 + 2) + 3 = (2 + 3) + 1 = (1 + 3) + 2* * * * *NO! The above answer is conflating the associative and commutative properties.The associative property for addition states that(a + b) + c = a + (b + c)The order in which the operations are carried out does not matter. And, as a result, either can be written, without ambiguity, as a + b + cThe associative property DOES NOT state that a + b = b + a. The order of the terms DOES matter. For that you need the operation to be commutative.There are mathematical operations that are associative but not commutative (matrix multiplication, for example).When elements are grouped without change of order, as:(a+b)+c=a+(b+c)
