BananaTrifleViolin,

Actually a good example:

  • If you have AIDs (A) then you have HIV (B). True
  • You have HIV (B) if, and only if, you have AIDS (A). Not true
  • If you don't have HIV (B), then you don't have AIDs (A). True, and the actual inverse of "If A then B"; which is "If not B, then not A"
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