  Math Central - mathcentral.uregina.ca  Quandaries & Queries    Q & Q    Topic: binary operation   start over

5 items are filed under this topic.    Page1/1            Is this operation associative? 2014-01-14 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 2008-09-08 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? 2008-09-06 From Francesca:Determine whether the binary operation * defined is commutative and whether * is associative * defined on Z by a*b = a-b\ 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.     A binary operation 2007-07-31 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 2007-07-30 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.      Page1/1    Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.    about math central :: site map :: links :: notre site français