







Is this operation associative? 
20140114 

From patrick: Associative test: Can you explain the following to me?
Is the following operation associative?: x*y=x+y+1
1) x*(y*z)=x*(y+z+1)=x+(y+z+1)+1=x+y+z+2
2) (x*y)*z=(x+y+1)*z=(x+y+1)+z+1=x+y+z+2
The answer is yes as 1) = 2)
My specific questions are:
1) How x*(y*z)=x*(y+z+1)=x+(y+z+1)+1 ?
2) How (x+y+1)*z=(x+y+1)+z+1?
Thank you!! Answered by Penny Nom. 





An associative binary operation 
20080908 

From Skye: Suppose that * is an associative binary operation on a set S. Show that the set H={a E S such that a*x=x*a for all x E S} is closed under *. (We think of H as consisting of all elements of S that commute with every element in S.)
Thanks! Answered by Harley Weston. 





Is this operation associative? 
20080906 

From Francesca: Determine whether the binary operation * defined is commutative and whether * is associative
* defined on Z by a*b = ab\
I understand how to figure out if it's commutative, but I thought for a binary operation to be associative, it had to have at least three elements, so I don't know how to tell if this associative or not. Answered by Penny Nom and Victoria West. 





Associative or commutative? 
20070824 

From Terry: 5*(7*2)=(7*5)*2 Is this associative property or commutative ??? Both? Answered by Penny Nom. 





A binary operation 
20070731 

From sofia: Prove that if * is associative and commutative binary operation on a set S, then
(a*b)*(c*d) = [(d*c)*a]*b
for all a,b,c,d element in S. Assume the associative Law only for triples as in the definition that is, assume only
(x*y)*z = x*(y*z)
for all x,y,z element in S. Answered by Penny Nom. 





Binary operations 
20070730 

From jim: prove or disprove:
Every binary operation on a set consisting of a single element is both commutative and associative.
Answered by Penny Nom. 





Fill in the blanks 
20061004 

From Justin: 1. To find out about how much, you can
2. The  states that the sum is the same no matter who you group the addends. Answered by Stephen La Rocque. 





Addends can be grouped differently but the sum does not change 
20020903 

From Jodia: I have been searching the web for over an hour & a half now for the answer to the following question: The _____ states that addends can be grouped differently but the sum does not change. Answered by Penny Nom. 





Definitions 
19970908 

From SohoGirl13: I am an 8th grader. my email address is SohoGirl13@aol.com. I have a question: what are the associative, communitive, and distributive properties? Answered by Harley Weston. 

