Submitted 9 months ago by Lafari@lemmy.world to [deleted]
An example of why this is wrong.
If a card is the ace of spades, it is black.
A card is black if and only if it is the ace of spades.
There are other conditions under which B (a card is black) can happen, so the second statement is not true.
A conclusion that would be correct is “If a card is not black, it is not the ace of spades.”. The condition is that if A is true B will also be true, So if B is false we can be sure that A is false as well - i.e. “If not B, not A”.
If Nazi, then fascist = true Fascist, if and only Nazi = not true
If car, then vehicle = true Vehicle if and only if car = not true
I used the bananas are fruits analog but your one works well too!
I just figured with Lemmy’s interest in politics it seemed like an obvious example. I threw in the car because I didn’t want to be that guy who makes everything about nazis…
If car, then vehicle = true
Car if and only if vehicle = true.
Is this correct?
Therefore “If A then B” = “A if and only if B” (or “If B then A” = “B if and only if A”)?
B can still be true when a is false. iff means that b can only be true when a is true.
You’d have to firm up your definition of car and vehicle before you could decide that one. Does a hot wheels car count as a car? Does a vehicle have to be large enough to move people or freight?
No
Is “If B then A” equal to “B if and only if A”?
No. They are effectively the same statement.
(A <=> B ) = (A=>B AND B=> A)
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 youre doing homework, i recommend writing out truth tables for the statements and comparing, gives you a bit more insight into the statement truth conditions
No.
Nope. The first statement doesn’t exclude any paths to B
I just saw a video on all the logical fallacies that exist, and this was one of them but my shit-ass memory can’t recall what the name of the fallacy was.
It's Cunningham's Fallacy.
I think it’s affirming the consequent
You got you logic screwed. What other if is there except for “if and only if”? I mean if I say “if” it’s only supposed to be true if its true.
The rest boils down to it’s the same statement. “if A then B” and “B if A” are the same.
^NP = P^
Is "if it snows school is closed" equal to "if school is closed it snows"
This is African rain dance logic
No. "In outer space, there is no atmosphere" does not mean "if there's no atmosphere, it must be outer space" - it could be a vacuum tube or something similar.
Boinkage@lemmy.world 9 months ago
No. It is equal to “if not B, then not A.” You’re welcome for doing your logic 101 homework for you.
pineapplelover@lemm.ee 9 months ago
First thing I thought lmao. Somebody is taking logic
XeroxCool@lemmy.world 9 months ago
That’s not equivalent either. “if not b, then not a” works if it’s a sequence but doesn’t work for options in which multiple inputs can lead to the same output. If you get pizza every Tuesday and Friday, then answering “what’s for lunch” with “if Tuesday, then pizza” and “if Friday, then pizza” doesn’t let it work in reverse. “what day is it” can’t be answered with “if pizza lunch, then Tuesday”
Boinkage@lemmy.world 9 months ago
Ya wrong.
If Tuesday, then pizza. And, if Friday, then pizza.
The contrapositive : if not pizza, then not Tuesday and not Friday.
What day is it? We’re not having pizza. So it’s not Tuesday or Friday.
pruwybn@discuss.tchncs.de 9 months ago
You left out the “not” part - “If not pizza lunch, then not Tuesday” does indeed work.
kogasa@programming.dev 9 months ago
Using standard definitions from propositional logic they are equivalent.
monotremata@kbin.social 9 months ago
Honestly what the homework is probably looking for is that it's equivalent to "B or not A." But yeah.