Topic: binary operation list of topics
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	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.

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