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The associative and commutative are properties of operations defined on mathematical structures.
Both properties are concerned with the order - of operators or operands.
According to the ASSOCIATIVE property, the order in which the operation is carried out does not matter. Symbolically, (a + b) + c = a + (b + c) and so, without ambiguity, either can be written as a + b + c.
According to the COMMUTATIVE property the order in which the addition is carried out does not matter. In symbolic terms, a + b = b + a
For real numbers, both addition and multiplication are associative and commutative while subtraction and division are not. There are many mathematical structures in which a binary operation is not commutative - for example matrix multiplication.
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How are associative and commutative proerties alike and different?
They are alike in so far as they are properties of binary operations on elements of sets. T The associative property states that order in which operations are evaluated does not affect the result, while the commutative property states that the order of the operands does not make a difference. Basic binary operators are addition, subtraction, multiplication, division, exponentiation, taking logarithms. Basic operands are numbers, vectors, matrices.
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