Is "If A then B" equal to "B if and only if A"?Lafari@lemmy.world to No Stupid Questions@lemmy.world – 40 points – 5 months ago60Post a CommentPreviewYou are viewing a single commentView all commentsYou'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.Not just HIV, but full blown AIDS?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" It's important to stress the "full blown" modifier in any example.
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.Not just HIV, but full blown AIDS?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" It's important to stress the "full blown" modifier in any example.
Not just HIV, but full blown AIDS?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" It's important to stress the "full blown" modifier in any example.
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" It's important to stress the "full blown" modifier in any example.
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.
Not just HIV, but full blown AIDS?
Actually a good example:
It's important to stress the "full blown" modifier in any example.