November 7th, 2010, 09:01 AM  #1 
Newbie Joined: Nov 2010 Posts: 4 Thanks: 0  binary composition
my question is like that let S be a set of atwo elements.how 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 8.bt i dont know how to solve it.in my opinion there can be only two binary composition.pls give a solution to this problem. 
November 7th, 2010, 09:06 AM  #2 
Senior Member Joined: Oct 2009 Posts: 105 Thanks: 0  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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