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MATH.17:2 - Problem

An operation can be permissible on its own yet leave the permitted class when combined with another. A transformation of operations can produce a valid operation yet alter the result of a sequence. These failures occur at different places: membership, composition, or the proposed transformation.

To locate the failure, specify the rule’s domain, construction and relevant laws. These supply the mathematical questions: which operations belong to the permitted collection, what can be done with them, and which conclusions follow?