March 12th, 2011, 12:32 AM  #1 
Newbie Joined: Mar 2011 Posts: 3 Thanks: 0  I want answer
let G be a set containing n elements. Find the number of binary operations on G .How many of them are commutative? I will be grateful to you if you answer this problem. thanks 
March 12th, 2011, 01:54 PM  #2 
Senior Member Joined: Nov 2010 Posts: 502 Thanks: 0  Re: I want answer
What work have you tried so far?

March 12th, 2011, 04:30 PM  #3 
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: I want answer
How many binary operations in total? I'd look at the operation f(x, x) for each of the n elements x, then look at the operation f(x, y) for x not equal to y. 
March 13th, 2011, 03:14 AM  #4 
Newbie Joined: Mar 2011 Posts: 3 Thanks: 0  Re: I want answer
binary operation is XxX to X where XxX has n square , and X has n elements. Then the number of this binary operation is unknown.

March 13th, 2011, 12:40 PM  #5  
Global Moderator Joined: Nov 2006 From: UTC 5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms  Re: I want answer Quote:
If you know the value of f(x, x), and you know that f is commutative, does that tell you anything about f(y, z) if y ? x or z ? x? How about f(x, y) with x ? y... does that tell you anything about f(w, z) with w ? x or z ? y, assuming f is commutative?  

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