#2 + a + b = a + 2 + b# is an example of which algebraic property?

1 Answer
George C.
Oct 25, 2015

It is an example of at least two algebraic properties:

Commutativity and associativity.

Explanation:

Addition is:

Commutative: #A+B = B+A#

Associative: #(A+B)+C = A+(B+C)#

The example #2+a+b = a+2+b# uses commutativity to get #2+a = a + 2# and hence #2+a+b = a+2+b#.

The example also uses associativity to even write #2 + a + b#. Without associativity, we would need to write: #(2+a)+b# or #2+(a+b)#, etc.

The example also expresses equality, which might also be counted as an algebraic property, but is often just assumed.

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