YOU are better than YOU think. Show yourself  how:

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 Logic Mastery
 Amazing, Amusing, Amorous,  Delicious, Delightful, Edifying, Strengthening Elixir. 
It eases work & learning difficulties Makes the hard easier. Opens eyes. Leads to greater precision.
in reading and writing

Do not leave here without it -  Logic mastery  will develops critical thinking, improve reading and writing, and give a firmer base for work and studies at many levels. Good luck.

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After logic,   (a) continue reading Three Skills for Algebra, chapters 8 to 14  and do so alongside site area on solving linear2007 Equations ; or (b) see this calculus starter lesson and Volume 3, Why Slopes  & More Math, chapters 2 to 6;

For online automated help in senior high school maths & calculus, visit  quickmath.com  For Automatic Calculus and Algebra Help with derivatives, integrals, graphs, linear equations, matrix algebra, visit calc101.com  With  overlap, each site quickmath & calc101offers a different range of services, some free, some not, all based on webmathematica. Good luck.

Explore collaborative whiteboards from groupboard,  twiddla  or scriblink.

Explaining the difference between the meaning of If A then B and   B if and only A is the purpose of the following two logic puzzles.  The questions in the puzzle below are intended to introduce and emphasize the difference.

Suppose the following:

1. the local store sells a newspaper if John enters.
2. the same store sells a newspaper if Jeremy enters.

Then we cannot state

the local store sells a newspaper if and only if John enters it (the local store). .

since the local store also sells a newspaper if Jeremy enters.

So there is a difference in meaning between the two suggestions or statements

1. the local store sells a newspaper if John enters.
2. the local store sells a newspaper if and only if John enters it (the local store). .

Seeing the difference in meaning in this simple example  is the key to precision reading and writing.

More generally,  there is a difference in meaning between the two suggestions or statements

• situation B  arises if and only if situation A arises
• situation B  arises if situation A arises.

Here we may say occurs or happens instead of arise, or omit the word arise altogether. That be said and done, we make the convention that the two statements

• Situation B  if situation A  (B if A form)
• If situation A then situation B (if A then B)

have the same meaning.

 Here we assume that the two following two statements have the same meaning:

• B if and only if A,
•  A if and only B

 mean the same. 

 Understanding there is a  difference in meanings is the key to greater precision and exactness in work and study.  If you see the difference, you will we hope make an effort to respect the difference and use the difference in following and writing rules or instruction. 

Postscript: October 2006. We may know the following:

Situation A occurs if situation B occurs

We may not know if there are furthers situations C such that

Situation A occurs if situation C occurs.

When further such situations C are possible. we cannot use the two-way implication rule

Situation A occurs if and only if situation B occurs.

The foregoing observation provides an alternative starting point