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 Sujet: binary operation
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 Is this operation associative? 2014-01-14 patrick pose la question :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!!Penny Nom lui répond. An associative binary operation 2008-09-08 Skye pose la question :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!Harley Weston lui répond. Is this operation associative? 2008-09-06 Francesca pose la question :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.Penny Nom and Victoria West lui répond. A binary operation 2007-07-31 sofia pose la question :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.Penny Nom lui répond. Binary operations 2007-07-30 jim pose la question :prove or disprove: Every binary operation on a set consisting of a single element is both commutative and associative. Penny Nom lui répond.

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