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 March 12th, 2011, 01:32 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, 02:54 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, 05:30 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, 04:14 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, 01:40 PM   #5
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Quote:
 Originally Posted by mahmoud 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.
How many pairs (x, y) are there in X x X with x = y? How many are there with x ? y?

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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