Question

a+(b+c)=(a+b)+c represents ________ property of addition of integers

Answer 1

Answer:

Hey mate here is your answer

Step-by-step explanation:

Associative property

In mathematics, the associative property[1] is a property of some binary operations. In propositional logic, associativity is a valid rule of replacement for expressions in logical proofs.

Within an expression containing two or more occurrences in a row of the same associative operator, the order in which the operations are performed does not matter as long as the sequence of the operands is not changed. That is, (after rewriting the expression with parentheses and in infix notation if necessary) rearranging the parentheses in such an expression will not change its value. Consider the following equations:

{\displaystyle (2+3)+4=2+(3+4)=9\,}(2+3)+4=2+(3+4)=9\,

{\displaystyle 2\times (3\times 4)=(2\times 3)\times 4=24.}2\times (3\times 4)=(2\times 3)\times 4=24.

Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".

Associativity is not the same as commutativity, which addresses whether or not the order of two operands changes the result. For example, the order does not matter in the multiplication of real numbers, that is, a × b = b × a, so we say that the multiplication of real numbers is a commutative operation.

Associative operations are abundant in mathematics; in fact, many algebraic structures (such as semigroups and categories) explicitly require their binary operations to be associative.

However, many important and interesting operations are non-associative; some examples include subtraction, exponentiation, and the vector cross product. In contrast to the theoretical properties of real numbers, the addition of floating point numbers in computer science is not associative, and the choice of how to associate an expression can have a significant effect on rounding error.

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Answer 2

Answer:

a+(b+c)=(a+b)+c represents associative property of addition of integers

Step-by-step explanation:

• The associative possessions of integers under accumulation and multiplication conditions that the derivative of the addition and expansion of better than two integers exists always the same irrespective of the grouping of integers. This indicates that for any three integers a, b, and c, we contain,

• a + (b + c) = (a + b) + c = (a + c) + b

• The associative property of integers accomplishes not hold valid for subtraction and division of integers, as, in the possibility of subtraction and division, the declaration of the numbers exists important and cannot stand adjusted.

Hence,

a+(b+c)=(a+b)+c represents associative property of addition of integers

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