Sorry for the inane post but I could really use some clarification here

I can prove it's false.

April showers = p
May flowers = q

first sentence is:
p => q

second sentence is:
not p => not q

now check if those two things are equivalent (they are not).

and as said, there can be another reason why flowers aren't blooming. for example, bee population completely gone or nuclear bomb. it's just a coincidence that it didn't rain that month then since no flowers could have bloomed anyway.

but the premise is that the first and second statements must always be satisfied, the only way that's possible is if p is equivalent to q

aka p=>q ^ q=> p == pq

False, because it is not a reason, let alone the only reason.

and that would be equivalent if p => q and q => p
the statements aren't set up that way though.
implication isn't commutative.

don't mind me, I can't read for shit.

statement 1: AS => MF
contrapose: ~MF => ~AS
premise of 17: ~MF == TRUE
this means TRUE => ~AS
ergo: ~AS must equal TRUE or the implication fails

>when it rains, flowers bloom
>when it doesn't rain, flowers do not bloom

How else would you describe an exclusive condition?

jesus are you all fucking trolls

statement 1: p=>q
statement 2: ~p=>~q
contrapose statement 2: q=>p

So the book presents you with that passage about rain, asks about rain, but the answer is based on other, outside possibilities that don't involve rain?
Yeah, it's 'merely possible' if you take into account other things like soil, the possibility of someone else watering the flowers, etc. But that's thinking outside the box bullshit.

you make zero fucking sense

no other factors can possibly matter based on the statements... the only possibility would be something like april showers happening, may flowers blooming, and then someone coming along and plucking all the flowers after they bloomed so they're not there anymore... yet why the fuck should someone consider that possibility

may flowers do not bring april showers

what makes no sense?

Exactly. The only factors that matter are the ones presented to you. And the only thing given to you is:
>if it rains, flowers bloom. if it doesn't they don't.
So a 'possible' answer to that, taking only the rain into consideration, is wrong, and so is the book.

"the implications say different things so anything goes"

False. The only things you can know from the statements are
1. if there are april showers, then there are may flowers
2. if there arent may flowers, then there arent april showers
3. if there arent april showers, then there arent may flowers
4 if there are may flowers, then there must've been april showers

None of these statements speak to other causes of a lack of may flowers.

the contrapositive of the first statement is that if there aren't may flowers, then there werent april showers (which doesn't imply anything about why may flowers may not bloom)

so we're not allowed to contrapose implications?

and anyone else thinking false:

it seems like the only basis for your arguments is that formal logic cannot and therefore should not be applied to this task.. is this true?

can someone please try to refute this?? nothing any of the falsers claim has spoken to this

Yes. You can't make a statement like "there exists no other cause" because that's simply something you can't know. It may seem trivial because the statements do bind april showers to may flowers, but it doesn't speak at all to the general set of possibilities. The statement "there exists no other cause" however, does speak to the general set of possibilities (but you don't know about the whole set).

Unsure if you're doing this as part of a computer science curriculum or not, but on a side note the importance of distinguishing between what you do and don't know in a whole set becomes really important in a lot of fundamental theory.

conversion error

*converse error, sorry. not my native language.

en.wikipedia.org/wiki/Affirming_the_consequent

it just kinda sounds like you're arguing for the possibility of divine intervention obstructing the implications.. is that what they teach comp sci students?

holy fucking shit seriously go fuck yourself

>Yeah, it's 'merely possible' if you take into account other things like soil, the possibility of someone else watering the flowers, etc. But that's thinking outside the box bullshit.

It's literally not wrong though. Like it's not a matter of thinking outside the box, it's a matter of understanding axioms and sets. There's a universal set of possible causes and none of these statements speak to april showers being the only cause of may flowers, it's simply wrong to suggest that's the case.
Falser here

April showers are indeed a subset of May flowers. Accordingly, you can't claim that a lack of april rain is the only reason may flowers dont bloom (if that was the case may flowers would be a subset of april showers).

It is merely possible because while the two are biconditionally related the statement in question 17 is making claims about other causes that haven't been written about in the premises (i.e. "the only reason" can be interpreted as excluding every other possible cause in the set of all causes). It's possible, because we don't know anything about the other possible causes (i.e. whether they do or don't cause flowers to bloom)

it would be p=>q; ~q, therfore ~p, which is valid by the implication

the complement of may flowers IS a subset of the complement of april showers

based on statement 2 may flowers is indeed a subset of april showers (:

Nope, it's called abstraction. OP is looking at formal logic. None of the premises speak about the set of all possible causes, however question 17 does make a claim about all possible causes. That's simply unwarranted.

Think of it this way:
Suppose the set of all possible considerations is as follows: U={A,B,C}

If I tell you

1. if B then C, and
2. if C then B,

can you conclude that if A then C is untrue? Of course not. I never said anything about A. This is the same situation

Oh by the way, here's the relevance in computer science if you're interested

wikiwand.com/en/Halting_problem

what you're literally saying is that if the soil is bad, and this means there are no may flowers, then this would have to also mean that there were no april showers, i.e. bad soil implies no april showers... is this seriously a valid conclusion in your mind

no it would be p=>q; ~p, therefore ~q. which isn't valid by truth tables.

"A is the only reason for B" == "B only if A" == B=>A which is equivalent to the contraposition of statement 2

It's a logical conclusion. Sure bad soil implies no april showers, but does it imply that bad soil wasn't the cause of the lack of may flowers? Of course not. It's possible to have multiple causes in this scenario.

statement 1****

True. Rains ALWAYS cause flowers, all other factors don't matter, lack of rains causes lack of flowers. So yes, lack of rains is the only reason for lack of flowers, because if there were rains, there would be flowers.

B only if A simply implies that if C causes B, then C must also cause A. However, it doesn't speak to whether or not C actually can or can't cause B.

See this post:

how can the state of the soil imply anything about the weather.... unless they are all equivalent in which case this whole argument is completely arbitrary because why would we just assume the possible existence of another equivalent condition and then say "no this new assumed equivalent condition is the actual reason"

>all other factors don't matter
all factors do matter if you're making a claim about all factors. Yes, a lack of may flowers will always be accompanied by a lack of april showers, but you still don't know anything about other causes (q17 is making the claim that ALL these other non-shower related causes cannot cause a lack of may flowers, which we simply can't conclude).

what the fuck are you talking about
with these two
p => q
not p => not q
you have fucking equivalence, p q
if there's any reason there aren't may flowers, it's equivalent to there not being april showers

If there are other possible causes of "no flowers", then it must be possible for it to rain and to not have any flowers, because no rain isn't the only cause no flowers.
That contradicts the statements.

are you saying that there could be a subset of april showers that, if true, would create the domino effect as the original "cause"? because then I actually may be on board...

In your previous post you said
>what you're literally saying is that if the soil is bad

If we're going with this assumption then we can make assumptions about the weather (as the soil being bad -> no may flowers and no may flowers -> no showers)

The textbook said "possibly" because we don't actually know anything about soil and what it does.
The point is that although may flowers and april showers go together, q17 is making a statement that every other cause that isn't april showers can't cause may flowers. That's simply unknowable, as we know nothing of the other causes.

See this: The biconditional only implies that if there are no may flowers there are no april showers, it doesn't speak to other causes and how they relate to a lack of may flowers however.

Yup exactly that. It doesn't matter if april showers will always accompany may flowers, what matters is that other stuff can cause it too (potentially)

you literally just said that lack of flowers in may can retroactively prevent rain from happening in april....

i still think it's bullshit to be expected to assume a possible cause of april showers as the genesis of the problem and therefore the legitimate "cause" but whatever fuck me i guess

A lack of may flowers does imply a lack of rain (contrapositive of statement one)

It's not because a big part of logic is understanding what you can and can't conclude from the given statements. q17 is a super broad statement, it's literally saying that NOTHING can cause a lack of may flowers, which is pretty crazy cause it's saying literally everything but april showers is unrelated to may flowers. Unless it used the word "only" somewhere we can't make such broad claims about a universal set.

that's an inverse fallacy.

p = it's snowing
q = it's cold

if it's snowing, then it's cold (p => q)
it's not snowing (not p).
therefore it's not cold (not q) (this statement is bad because it can be cold without snow).

In other words if we do not assume the premises to be true when it's true, the premises have become circumstantial.

yes but he's saying the lack of may flowers itself was already caused by SOMETHING ELSE and THEN makes it so there are no april showers, which were NOT the cause of the no may flowers

In the problem it is given:
p => q is True
AND
~p => ~q is True

What you're saying is:
p => q is True
~p is True

there are two inverse statements given fuckhead, inform yourself of the situation before you make idiotic posts

>that's an inverse fallacy
no it's fucking not
~p => ~q is equivalent to q => p
that, along with p =>q, gives you q p

Nono the premises are true. Like, we're assuming the premises are 100% true. It's just that none of the premises talk about "everything else", but q17 does make a claim about "everything else" (i.e. "everything else" isn't a cause of a lack of may flowers). q17 is a statement made totally out of the scope of the premises. Yes you can conclude that whenever there are no may flowers there are no april showers, but you can't conclude that nothing else can cause no may flowers. (because nothing else=everything else=stuff not addressed in the premises).

Yup, which is fine. The linearity of events doesn't matter. What matters is that you can conclude IF there are no may showers, then there mustn't have been april showers. Sure, you can say "those lack of april showers caused the lack of may flowers" but it's also totally possible that some external event caused a lack of april showers which in turn caused a lack of may flowers (and so you can say that if that external event occurred, it would cause a lack of may flowers).

that's not what the guy said at all but it is what i already said in an earlier post so thanks genius

but the way you phrased that still labels april showers as the cause of no may flowers specifically, and the question doesn't ask for the cause of the april showers so...

I have a ball.
If I hold the ball, it will stay in my hand.
If I do not hold the ball, it will not stay in my hand.
I did not hold the ball.

Is it true that my not holding the ball was the only reason it didn't stay in my hand?

>and so you can say that if that external event occurred, it would cause a lack of may flowers).
But only through lack of showers. Direct reason for lack of flowers is always lack of showers.

That's exactly what I said (I've been the same person replying to you this entire time btw).

I said
> (as the soil being bad -> no may flowers and no may flowers -> no showers)

Which isn't wrong (no may flowers implies no showers).

The statement in q17 doesn't say "april showers don't cause may flowers", it said "there is NOTHING else that causes may flowers". Which is unknowable.

If I have these 3 statements:
1. If A then B (A->B)
2. If B then C (B->C)
I can very simply conclude that If A then C. Right? It's one of those elementary logic examples they use when introducing this stuff. This conclusion says that A is a cause of C, even if indirectly. Q17 would posit that because B->C and C->B then A->C is untrue, but of course thats unknowable (it didn't make any statements about A).

Sure, but that doesn't deny that the external event was a cause. Q17 isn't saying april showers arent the cause of may flowers, it's saying that the external event couldn't have caused the may flowers.

See: