IB Maths HL Option Sets Binary operations

Operation table of a group, Symmetries of plane figures, Cycle notation for permutations, Left and right cosets, group homomorphism, kernel, kernel and range of a homomorphism, isomorphisms

IB Maths HL Option Sets Binary operations

Postby elizabeth » Thu Mar 07, 2013 7:38 pm

IB Mathematics HL Option: Sets, Relations and groups (Binary operations)


How can we show if the following binary operation on R defined be x*y=xy+4 is commutative or associative.

Thanks
elizabeth
 
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Re: IB Maths HL Option Sets Binary operations

Postby miranda » Thu Mar 07, 2013 7:51 pm

IB Mathematics HL Option Sets, relations and Groups - Binary operations

Since x*y=xy+4 and y*x=yx+4= xy+4= x*y, the operation is commutative.
(x*y)*z=(xy+4)*z=(xy+4) z+4=xyz+4z+4
x*(y*z)=x*(yz+4)=x (yz+4)+4=xyz+4x+4 which is different than (x*y)*z
thus the binary operation * is not associative.
miranda
 
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