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 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.
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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)=x*(yz+4)=x (yz+4)+4=xyz+4x+4 which is different than (x*y)*z
thus the binary operation * is not associative.
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