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 on it.

This page is not in its usual appearance because WIMS is unable to recognize your web browser.

In order to access WIMS services, you need a browser supporting forms. In order to test the browser you are using, please type the word wims here: and press ``Enter''.

Please take note that WIMS pages are interactively generated; they are not ordinary HTML files. They must be used interactively ONLINE. It is useless for you to gather them through a robot program.

Description: collection of training exercises on necessary and sufficient conditions. This is the main site of WIMS (WWW Interactive Multipurpose Server): interactive exercises, online calculators and plotters, mathematical recreation and games

Keywords: wims, mathematics, mathematical, math, maths, interactive mathematics, interactive math, interactive maths, mathematic, online, calculator, graphing, exercise, exercice, puzzle, calculus, K-12, algebra, mathématique, interactive, interactive mathematics, interactive mathematical, interactive math, interactive maths, mathematical education, enseignement mathématique, mathematics teaching, teaching mathematics, algebra, geometry, calculus, function, curve, surface, graphing, virtual class, virtual classes, virtual classroom, virtual classrooms, interactive documents, interactive document, logic, necessary,sufficient