c(a*b) = (c*b)a
Is this commutative, associative, or both? It feels like it is commutative since numbers change their order. However, it feels like it is associative, because different numbers are grouped together in the parenthesis. Is it possible to show two properties at once?
c*(a*b) = (c*a)*b is associative
c*(a*b) = c*(b*a) is commutative
c*(a*b) = c*(b*a) = (c*b)*a is both
communative.
To determine whether the given expression is commutative, associative, or both, let's break it down:
The expression is: c(a * b) = (c * b)a
1. Commutative property: This property applies to operations that can be interchanged without affecting the result. In the given expression, the order of the numbers inside the parentheses and outside the parentheses changes. Since the order changes, we can conclude that the expression is NOT commutative.
2. Associative property: This property applies to operations where the grouping of numbers can be changed without affecting the result. In the given expression, we have two sets of parentheses: (a * b) and (c * b). If c is multiplied by (a * b) first and then multiplied by 'a', or if (c * b) is multiplied by 'a', the result is the same in both cases. Therefore, the expression is associative.
In conclusion, the expression c(a * b) = (c * b)a is NOT commutative, but it is associative. It is possible for an expression to exhibit multiple properties simultaneously, so in this case, we have both commutative and associative properties being considered.