Keep the direction of the rule
“If a document is classified, it requires secure storage” says that classification is sufficient for a secure-storage requirement. It also makes the storage requirement necessary for being a classified document under this rule. It does not say that everything needing secure storage is classified. Other sensitive materials could need it as well.
The contrapositive preserves the rule: if no secure-storage requirement applies, the document is not classified. Reverse and negate both sides. Simply reversing the original rule is invalid, as is concluding that an unclassified document has no secure-storage requirement. Both mistakes ignore other ways that requirement might arise.
Translate only, unless, and exceptions
“Only registered visitors may enter” makes registration necessary for permitted entry: permitted entry implies registration. It does not guarantee that every registered visitor may enter. “Every registered visitor may enter” would make registration sufficient instead. Under ordinary inclusive use, “a permit is required unless the event is exempt” means that an event which is not exempt requires a permit; it does not promise that exempt events never need permits for another reason.
Read the scope of a rule and its exceptions together. “All public meetings must be announced, except emergency sessions” does not establish a rule for private meetings. A claim that an action is permitted is also different from a claim that it is required. These distinctions matter when applying organizational policies as much as when solving formal exercises.
Quantifiers control what can follow
All means every member of the stated group; some means at least one and can include all. “Some editors are historians” converts to “some historians are editors.” “All editors are historians” does not convert to “all historians are editors.” In modern logic, an all-statement alone also need not establish that the group contains anyone.
Most means more than half. If most members are writers and most members are speakers, the two groups overlap, assuming the same finite group of members. If merely some members are writers and some are speakers, they need not overlap. Percentages require a denominator: a larger share of a smaller group may still contain fewer people.
Worked example
Only accredited reporters receive press passes. Every recipient of a press pass may enter the media room. Maya entered the media room.
- First rule
- Press-pass recipient implies accredited reporter. “Only” marks the requirement, not an entitlement.
- Second rule
- Press-pass recipient implies permission to enter the media room.
- What does not follow
- Maya’s actual entry does not establish that she had a press pass, was accredited, or even had permission. Other entry rules or unauthorized entry remain possible.
- A valid application
- If Noah received a press pass, both accreditation and permission to enter follow from the rules.
Check your understanding
Take it into practice
Write “if … then …” in ordinary words, then check that you have not reversed the rule or changed permission into obligation.