Anonymous at Thu, 10 Oct 2024 21:33:22 UTC No. 16419841

>>16419810
P if Q: Q implies P.
P only if Q: P implies Q.
P if and only if Q: P implies Q and Q implies P (P and Q are equivalent).

Anonymous at Thu, 10 Oct 2024 21:38:43 UTC No. 16419847

>>16419841
I think you got "if and only if" wrong

Anonymous at Thu, 10 Oct 2024 21:49:22 UTC No. 16419853

>>16419810
if only...

Anonymous at Thu, 10 Oct 2024 22:08:44 UTC No. 16419865

>>16419847
In what way?

Anonymous at Thu, 10 Oct 2024 22:10:55 UTC No. 16419869

>>16419865
Specifically "P and Q are equivalent." While it's true that they imply each other that doesn't mean they are "equivalent."

Source: university mathematics

Anonymous at Thu, 10 Oct 2024 22:29:02 UTC No. 16419881

>>16419810
[If "X", then "Y"] would mean X guarantees Y to happen, but so could possibly A,B,C,D..etc.

[Only if "X" then "Y"] would mean X has to happen for Y to happen, but doesn't guarantee it as opposed to above. In this case X is just required. So X could by itself cause "Y", but it might be a combination of "X" and "A" and "C" that is needed to cause "Y"..etc. However, whatever the case, "X" has to be part of the equation.

[If and only if "X" then "Y"] could combine both above and make "X" the sole cause of "Y". It's like just "If" but without the possiblility of A,B,C,D..etc. also causing "Y".

[If and only if "X" then "Y"] is the only time where you can pinpoint the exact cause of "Y" backwards.
With just "If", the cause could be anything. With just "only if", you only know "X" is part of the cause but don't know for sure if there is anything else involved.

Anonymous at Thu, 10 Oct 2024 23:17:47 UTC No. 16419964

>>16419869
>While it's true that they imply each other that doesn't mean they are "equivalent."
>Source: university mathematics
Must be a shitty university, because iff is an equivalence relation.

Anonymous at Thu, 10 Oct 2024 23:27:22 UTC No. 16419984

You can even meaningfully talk about set partitions on the space of mathematical statements using Gödel’s autistic formulation of mathematical logic if you really wanted to.

Anonymous at Thu, 10 Oct 2024 23:36:14 UTC No. 16420001

You will only understand "if and only if" only if you understand "only if", but not if and only if you do.

Anonymous at Thu, 10 Oct 2024 23:45:44 UTC No. 16420015

>>16419810
If I perform my ritual dance, the sun will rise tomorrow. (My dance was sufficient but not necessary.)
Only if I track down this animal can I kill it. (Tracking was necessary but not sufficient.)
If and only if I let go of this rock, it will fall to the ground. (Letting go was necessary and sufficient.)

Anonymous at Sat, 12 Oct 2024 00:44:31 UTC No. 16422043

>>16419810
Discrete math is shit.
I hate logic
>inb4 low iq filtered
I got an A in discrete math

Anonymous at Sat, 12 Oct 2024 04:19:58 UTC No. 16422284

>>16419810
there is no difference

Anonymous at Sat, 12 Oct 2024 05:53:08 UTC No. 16422413

>>16420015
Help me out.
Suppose you use the dance example for all three.
>Only if I perform my ritual dance, the sun will rise tomorrow.
>If and only if I perform my ritual dance, the sun will rise tomorrow.
I don't see how the dance is not sufficient in the "only if" category.
I think anon>>16422284 may be right.

Anonymous at Sat, 12 Oct 2024 10:20:15 UTC No. 16422570

>>16422043
>he cites his grades
low IQ indeed

Anonymous at Sat, 12 Oct 2024 13:06:05 UTC No. 16422690

>>16422413
>>Only if I perform my ritual dance, the sun will rise tomorrow.
>>If and only if I perform my ritual dance, the sun will rise tomorrow.
but the sun will rise even if you don't do the sun dance, so both of these are wrong

Anonymous at Sat, 12 Oct 2024 13:09:52 UTC No. 16422694

>>16420015
if you throw the rock up it will still fall to the ground desu senpai

Anonymous at Sat, 12 Oct 2024 13:17:45 UTC No. 16422701

>>16419810
If and only if

What's there to not understand?

If oreo then milk. If oreo then only if milk.

Anonymous at Sat, 12 Oct 2024 13:32:00 UTC No. 16422719

>>16422694
you can't throw the rock without letting go of it my smarmy cunt friend

Anonymous at Sat, 12 Oct 2024 13:55:27 UTC No. 16422737

>>16422719
letting something go doesn't refer to throwing it it refers to dropping it

Anonymous at Sat, 12 Oct 2024 14:25:11 UTC No. 16422778

>>16419841
Can you come up with a specific example of why this works?. Use numbers or matrices etc. Something I can wrap my pea brain around. Thanks.

Anonymous at Sat, 12 Oct 2024 14:41:48 UTC No. 16422797

>>16419810

A if B
B causes A.

A only, if B
B causes A, but only A. It can't cause C, E, D, etc.

A if B and A only if B
This is just both the above
B causes A and B may only cause of A


A only if B
(Notice the lack of comma!)
This means B causes A and nothing else can cause A

A if and only if B
This means A only if B is the only cause of A.

Anonymous at Sat, 12 Oct 2024 14:44:51 UTC No. 16422801

Think of these as functions

A if B -> IF(A, B)
A only if B -> ONLYIF(A, B)
A if and only if B -> IF(A, B) && ONLYIF(A, B)

Anonymous at Sat, 12 Oct 2024 14:58:12 UTC No. 16422820

OP dont fret. I have 85 IQ and it took me about a week to understand it.

A IFF B implies B IFF A

PROOF:

A IFF B = B -> A & —B -> —A = True
That is
B -> A = True
—B -> —A = True

A -> B = —B -> —A (think about this)

A -> B = True (follows immediately)

—A -> —B = B -> A (think about this)

—A -> —B = True (follows immediately)

Therefore B IFF A

Anonymous at Sat, 12 Oct 2024 16:48:17 UTC No. 16423014

>>16422690
I get that, but assume that only if I do my dance the sun will rise (as if we live in an absurd world) how is that different from a world where if and only if I do my dance where the sun will rise?

Anonymous at Sat, 12 Oct 2024 19:10:41 UTC No. 16423352

>>16422570
>g-grades dont matter, I wasn't able to do simple equations to pass the test b-but I'm street smart!
IQlet detected.

Anonymous at Sat, 12 Oct 2024 19:39:12 UTC No. 16423409

I have always thought that it's just a language thing. I mean, like emphasizing a certain thing. Like saying something like "it is important, very important" but you might as well say just "very important" it's the same thing.

Anonymous at Sat, 12 Oct 2024 20:32:24 UTC No. 16423516

>>16422797
>A only, if B
>B causes A, but only A. It can't cause C, E, D, etc.
Bro..

Anonymous at Sat, 12 Oct 2024 20:47:56 UTC No. 16423539

>>16419869
they are logically equivalent,p iff q means that if one is true the other is true thus they are logically equivalent regardless of if they mean the same thing, they are corequisite thus they logically are equivalent

Anonymous at Sat, 12 Oct 2024 21:03:30 UTC No. 16423561

>>16423516
he should have said B causes A but C D and E etc. cant cause A

Anonymous at Sat, 12 Oct 2024 21:11:19 UTC No. 16423571

>>16423561
The "only if" says C,D,E..etc. can't cause A by themselves without B, that's it.
This whole thing doesn't say anything about whether or not B can cause anything else other than A. Nothing in all 3 tier logics says anything about this.

Anonymous at Sat, 12 Oct 2024 21:47:16 UTC No. 16423611

>>16423352
I TAed in grad school. You can literally give your students straight As and not bother grading. The profs don't care. And you as a PhD student save your time. Profs only care about you grading harshly because they might get negative feedback. I once had my supervisor tell me to bump the grade on a student's assignment so that they wouldn't fail. That's how meaningless all this shit it, Mr Bachelor.

Anonymous at Sat, 12 Oct 2024 22:21:02 UTC No. 16423661

I thought "and only if" just put my emphasis on the importance of the first if

Anonymous at Sat, 12 Oct 2024 22:30:49 UTC No. 16423672

>>16423571
>>16423561
>brainlets do not understand commas

Anonymous at Sat, 12 Oct 2024 22:32:19 UTC No. 16423676

>>16423672
>>16423561
>>16423516
> if B only A == A only if B

Anonymous at Sun, 13 Oct 2024 00:52:30 UTC No. 16423849

>>16419810
when you think about it "if" is the [math]\impliedby[/math] while "only if" is the [math]\implies[/math].
I swear I see textbooks mix this up constantly
>first we do the if part
and then they actually do [math]\implies[/math]

Anonymous at Sun, 13 Oct 2024 01:07:03 UTC No. 16423872

>>16423849
*** ligature moron detected ***

Anonymous at Sun, 13 Oct 2024 21:24:53 UTC No. 16429486

>>16422820