They're simply applying the rule for *. If the general rule is x'*y'=x'+y'+1, and you have x*(y+z+1) then you can match up x' with x and y' with (y+z+1):port31 said:Homework Statement
Im looking at this example and trying to figure out how they showed it was associative.
They start out with x*y=x+y+1
then they add in z to show it is associative.
x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2
I don't know how they go from this x*(y+z+1)=x+(y+z+1)+1
and end up with the equation on the right.
What do you mean you 'solved it'? The * doesn't stand for normal multiplication here. x*y=x+y+1 is defining an operation '*'.If i solved for x from x*y=x+y+1
Yes, associativity is a fundamental property in group theory. It allows us to combine three or more elements in a group in any order without changing the result.
A group is associative if the order in which elements are grouped in an operation does not affect the final result.
To determine if a group is associative, you can perform the associative property test. This involves grouping the elements in different ways and checking if the results are the same. If they are, the group is associative.
No, not all groups are associative. Some examples of non-associative structures include non-associative algebras and non-associative rings.
The set of integers under addition is an example of an associative group. This means that when adding three or more integers, the order in which they are grouped does not affect the final result.