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Comment on Is "If A then B" equal to "B if and only if A"?

Apepollo11@lemmy.world ⁨11⁩ ⁨months⁩ ago

You’ve have some examples, but in case they are not clear enough:

If [you have AIDS] then [you are unwell]

[You are unwell] if and only if [you have AIDS]

The first one is not the same as the second. Why? There are plenty of ways to be unwell, without necessary developing AIDS.

The first statement only defines one possible path to B, not all of them.

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AmidFuror@kbin.social ⁨11⁩ ⁨months⁩ ago
Not just HIV, but full blown AIDS?

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- BananaTrifleViolin@kbin.social ⁨11⁩ ⁨months⁩ ago
  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"; "If not B, then not A"
  
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  - AmidFuror@kbin.social ⁨11⁩ ⁨months⁩ ago
    It's important to stress the "full blown" modifier in any example.
    
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