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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=x+y-4 is commutative or associative.

Thanks

How can we show if the following binary operation on R defined be x*y=x+y-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=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.

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

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