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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

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

Thanks

- elizabeth
**Posts:**0**Joined:**Mon Jan 28, 2013 8:09 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.

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
**Posts:**268**Joined:**Mon Jan 28, 2013 8:03 pm

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