document.write( "Question 487933: How do you differentiate the properties associative,communitive, and distributive \n" ); document.write( "

Algebra.Com's Answer #333215 by richard1234(7193) $\"\"$ $\"About$

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For any binary operation * (not necessarily addition or multiplication):\r
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\n" ); document.write( "\n" ); document.write( "* is said to be associative if (a*b)*c = a*(b*c) for all a,b,c ∈ S (S is a set composed of all possible a,b,c)\r
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\n" ); document.write( "\n" ); document.write( "* is said to be commutative if a*b = b*a for all a,b ∈ S\r
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\n" ); document.write( "\n" ); document.write( "* is said to be distributive over another operation (I'll denote this operation by &) if a*(b&c) = (a*b)&(a*c) for all a,b,c ∈ S.\r
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\n" ); document.write( "\n" ); document.write( "For example, vector addition is commutative and associative, scalar products are distributive, the dot product of vectors is commutative, and the cross product of vectors is associative over vector addition, but not commutative (in fact, it is said to be anti-commutative, similar to subtraction). These are just examples of operations other than addition or multiplication that obey these properties. \n" ); document.write( "

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