The activity that relates to scrutiny or examination of a given problem is called Investigation.
Scrutiny refers to the act of inspection or examination into some important matter. For example:- Inspector doing the detail scrutiny of the crime matters.
The action that refers to scrutiny or the analysis of a certain topic is called investigation. When the unique issue requires careful analysis. A thorough investigation is conducted to have a full understanding of the issue.
Therefore, it can be concluded that investigation is step by step scrutiny of the problem.
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Your question is incomplete, but most probably the full question was....
A (an) ____ is a part-by-part scrutiny of a given problem.