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 7:37 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=x+y-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 7:50 pm

IB Mathematics HL Option Sets,relations and Groups (Binary operations)

Since x*y=x+y-4 and y*x=y+x-4= x+y-4= x*y, the operation is commutative.

(x*y)*z=(x+y-4)*z=(x+y-4)+z-4=x+y+z-8

x*(y*z)=x*(y+z-4)=x+(y+z-4)-4=x+y+z-8

thus the binary operation * is associative.
miranda
 
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