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| {{for|the rule of inference propositional logic which expresses Case analysis|Disjunction elimination}}
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| {{Unreferenced|date=December 2009}}
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| '''Case analysis''' is one of the most general and applicable methods of analytical thinking, depending only on the division of a problem, decision or situation into a sufficient number of separate cases. Analysing each such case individually may be enough to resolve the initial question. The principle of case analysis is invoked in the celebrated remark of [[Sherlock Holmes]], to the effect that when one has eliminated the impossible, what remains must be true, however unlikely it seems.
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| ==Connections with logical principles==
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| The logical roots of the Holmes remark speak to the principle of [[excluded middle]]. That indicates the importance to case analysis of [[logical disjunction]]: stringing together propositions with the [[logical connective]] ''"or"''. [[Medical diagnosis]] can indeed follow the Holmes pattern, with a patient's symptom possibly caused by a number of conditions: the patient suffers from ''A'' or ''B'' or ... or illness ''I''; see [[differential diagnosis]]. [[Deductive logic]] is applied to reducing the number of cases; see [[case-based reasoning]].
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| A canonical statement of case analysis in the sentential calculus is:
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| "If a statement ''P'' implies a statement ''Q'', and a statement ''R'' also implies ''Q'', and either ''P'' or ''R'' is true, then ''Q'' must be true."
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| : <math>(((P \rightarrow Q) \land (R \rightarrow Q)) \land (P \vee R)) \rightarrow Q \, </math>
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| ==Exhaustive analysis==
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| The most important issue in this style of case analysis is that the cases should be collectively ''exhaustive'': everything is covered. The condition that they should be ''exclusive'', while convenient, is not to be assumed lightly; for example a patient's liver problem might be caused by [[hepatitis]] ''and'' abuse of alcohol, with one factor not ruling out the other. This points up the distinction between [[exclusive or]], and logical disjunction which is the default meaning of 'or' (in logic, mathematics and science) and which is non-exclusive. Case analysis of the non-overlapping kind is a special case, only.
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| That being said, in [[computer programming]], case analysis presents itself in a form best adapted to exclusive cases. In simple terms, the requirement is to have a list of actions, so that 'if X = 1 do P, if X = 2 do Q, if X = 3 do R' can be given as quite unambiguous instructions. The value of X here is computed according to what case one is in.
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| ==Other terminology==
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| '''Case-by-case analysis''' is a more specific term for such a pinning-down of cases. It assumes a situation in which a thorough-going case analysis can be completed: all cases covered and resolved. This is not always realistic. Other forms of case analysis are [[best case analysis]] and [[worst case analysis]], scenarios for the optimist and pessimist, respectively.
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| Two names for approaches that take complete case-by-case analysis as not meeting the needs of the topic under consideration are [[casuistry]], most often in [[ethics]], and the [[case study]] method used in business schools.
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| ==See also==
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| *[[Mutually exclusive]]
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| *[[Collectively exhaustive]]
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| *[[Pattern matching]]
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| *[[Proof by exhaustion]]
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| {{DEFAULTSORT:Case Analysis}}
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| [[Category:Methods of proof]]
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| [[Category:Theorems in propositional logic]]
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