# Properties of Linear Operators

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In each of parts (a) and (b), an operation * is defined over the set of natural numbers. For each operation, determine these four things.

See Attachment.

Please provide detailed explanation showing all steps and reasoning as well as formal notation for the Proof.

Please post response as a MS Word or PDF file.

Thanks for your time!

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#### Solution Summary

Given several linear operators, we determine which are closed, associative, or commutative.

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