OEF iff --- Introduction ---

The notion of necessary conditions and sufficient conditions is of fundamental importance in the mathematical reasoning. For this reason, experts in such reasoning, including math teachers, often get so used to it that they do not realize how this notion may be difficult and unusual to students.

In fact this notion is not so difficult as it often appears to some students, and it is in practicing that one becomes expert. Therefore we gather here 11 training exercises on this notion, in a hope to quickly make you an expert

Three functions

, .
, , .
, .

Three functions II

, .
, , .
, .

Chained symbols

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If or only if

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If or only if II

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If or only if III

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If or only if IV

.

Parity

Subset

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Symbol

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Symbol II

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