If one thing (B) follows from something (A) that is sufficient, then that which follows (B) is a necessity for the something (A). (If that is confusing just keep reading it will be blatantly clear at the end.) A hidden assumption is a necessary condition that was not stated. If it is claimed that something is sufficient but it is not, this must lead to a logical contradiction once a rule is applied that is only applicable if the statement is indeed sufficient. If indeed B follows from A alone, then A can not be without B. But if in reality there is a side condition for B other than A, then A can be without B. This thinking can be used to check the completeness of assumptions. In a world were "(C and D) E", I might make the (false) claim: "C E" But from that follows that C can never be true if E is false. Knowing the world you might come up with a case were C can be true without E being true, then you found the counter argument and likely the side condition D that was not met in your counter case. Aside from checking arguments this is useful in checking technical requirements. "In the event of a crash the passenger air bag deploys." Therefore "If the airbag is undeployed there can not have been a crash." Now that is clearly wrong, thus the first statement must have been wrong.

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