• Apepollo11@lemmy.world
    181·
    1 year 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.

      • BananaTrifleViolin@kbin.social
        81·
        1 year 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”; which is “If not B, then not A”