Necessary and Sufficient conditions

[MathMaestro]

Hello Math Gurus, most everything I find on the web on Necessary and Sufficient are confusing. So let me know if this is correct.

I start with the standard conditional statements:

Statement: If P, then Q.
Inverse: If not P, then not Q.
Converse: If Q, then P.
Contrapositive: If not Q, then not P.

Therefore,

Necessary condition is when the Statement is true and the Contrapositive is true.
Sufficient condition is when the Statement is true and the Inverse is true.
If and only if condition is when the Statement is true and the Converse is true.

And you can have various combinations of the 3 conditions like "Necessary and Sufficient" or "Necessary but not Sufficient" or "If and only if but not Sufficient", etc.

Let me know if this is correct or confusing. The best site to support this is at
http://pages.pomona.edu/~mjg14747/001-2 ... ient.shtml

Thanks.

[MistaPotta]

[MathMaestro]

[MistaPotta]

Let's try something simpler.

If Jenny goes to the mall, she will buy a CD.

Going to the mall is a sufficient condition for her buying a CD.
Her buying a CD is a necessary condition for Jenny going to the mall.

In general, if p then q is true, then q is a necessary condition for p, and p is a sufficient condition for q.

[88bobcat]