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binary operations

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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.
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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