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November 7th, 2010, 09:01 AM   #1
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binary composition

my question is like that
let S be a set of atwo many different binary composition can be defined on S?how many different commutative binary composition can be defined on S?
the answers are 16 and i dont know how to solve my opinion there can be only two binary composition.pls give a solution to this problem.
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November 7th, 2010, 09:06 AM   #2
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Re: binary composition

Look at all of the possible combinations you can have with two elements. I'll give you a head start...

You can have the the binary operation where everything leaves the first element unchanged, that is,

a*b = a
a*a = a
b*a = a
b*b = b
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