#
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

.

### If or only if

.

### If or only if II

.

### If or only if III

.

### If or only if IV

.

### Parity

### Subset

.

### Symbol

.

### Symbol II

.

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- Description: collection of training exercises on necessary and sufficient conditions. interactive exercises, online calculators and plotters, mathematical recreation and games
- Keywords: interactive mathematics, interactive math, server side interactivity, logic, implication,reasoning