Also, one more thing of note to supplement what zippyandzap said:

Thinking of the contrapositive and plain jane *modus ponens*, i.e., a simple "If A then B" statement, as restating the same conditional under the different but related terms of necessary and sufficient conditions is very helpful. When we have, as a rule, that if A, then B (A-->B), we know in addition to A being sufficient for B, that B is necessary for A. Thus, since the property of B is necessary for A, if A obtains, B MUST obtain. Hence the contrapositive--if B does not subsist as a property of something x, then x cannot be A.

Hope this helps.

T