Teaching Myself - The Elements of Style (Comma joining two independent clauses)

The Elements of Style, the most respected and recommended book on writing, is a thin book. Just 100 odd pages. But I have already started having a feeling that my journey through this book is going to be a long one.

Today, I have just read about adding a comma before the conjunction which joins two independent clauses. Like:

The floods in Pakistan are an unfortunate natural calamity, and all countries are trying to extend help.
Apple has recently hired an expert in mobile payment technology, but the company has not publicly announced any plans to get into mobile commerce.

Similarly, if two independent clauses are separated by as, for, or, nor or while, a comma will be required.

An important variation to this rule: If a dependent clause or introductory phrase precedes the second independent clause, no comma is required after the conjunction.

The situation is difficult, but if we persist, there are still chances of succeeding in the mission.

Enough for the day!