I took a discrete math class but didn't attend at all and only read the day before the exam; didn't do very well. I got the general idea of the concepts and could grasp analogies, but couldn't solve anything beyond simple stuff. Should I drop the subject altogether?

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>when low in conscientiousness

how much time is reasonable to spend studying in order to be able to solve any non advanced discrete math problem thrown your way?

Nothing in undergrad math is hard boyo. Never go to class and study by yourself. Just show up for the exam, but do the work at home by yourself at least.

Almost nothing in any topic is hard.

Most of the things which people say are "hard" just require tedious and/or time consuming prerequisites and/or grinding.

It is an inclusive "or".

You are thinking of the exclusive "or", which would be:

p -> (¬r ^ p) v (r ^ ¬p)

I'm too lazy to write it in latex

the argument I posted still works if the or is exclusive. If not p is false then not r must be true.

> still works if the or is exclusive.

Inclusive*

>Almost nothing in any topic is hard.

If you have 120+ IQ. I don't think you have any idea how hard it is for normies to grasp Calculus.

What exactly is the hangup? It's just a bunch of rules for functions of real numbers.

the majority of the world's population can't even grasp something as simple as f(x)=y

>Almost nothing in any topic is hard.

Most of the things which people say are "hard" just require tedious and/or time consuming prerequisites and/or grinding.

what is actually hard then?

I think it's valid iff weak excluded middle holds, i.e. the axiom, for all A,

[math]neg Alorneg neg A[/math]

If you only want to check if something is classically valid, you can use

https://www.umsu.de/trees/#(p~5(~3r~2~3p))~5(~3r~2~3p)

>Implying we need some fancy non standard logic like WeAk eXcLudEd mIdDle

moron.

>Proof by cases

>Case 1. Assume q. Then not r or not P by (2)

>Case 2. Assume not q. Then not P by (1). Then not P or not r .

It's literally intro logic 1, third week of class.

That doesnt’t change the fact that you can use it to prove anything

If I woke up today I went to the bathroom

If I went to the bathroom I’m not alive right now or I didn’t wake up today

Therefore I’m not alive right now or I didn’t wake up today

But I did wake up today, so “I didn’t wake up today” is false. Hence “I’m not alive right now” must be true.

I'm also surprised you're still alive with a brain that moronic.

we need some fancy non standard logic like WeAk eXcLudEd mIdDle

Weak excluded middle is not non-standard, it's implied by excluded middle, which is valid in classical logic.

The restriction to weaker systems here is just helpful to highlight why the conclusion might seem counter-intuitive.

E.g. classical logic also proves, for any two statements A and B, that the following is valid

[math](Ato B)lor(Bto A)[/math]

So "Either me wearing blue socks right now implies that you wear red underpants right now, or you wearing red underpants right now implies that I'm wearing blue sock right now."

This is classically true by case analysis, but the arguably non-sensical nature of this "true" statement highlights the issue of taking the material implication for full as far as logical reasoning is concerned. Bivalent semantics work nice with integers, but fail you often as soon as you take formal logic from math to reasoning.

Restricting yourself to a weaker logic, e.g. intutionistic logic (which e.g. does not prove [math](Ato B)lor(Bto A)[/math]), leads you to theorems that are more commonly not full of pathologies like this.

You can prove OP's pic by case distinctions, and the link I gave essentially does just that.

My point is that it doesn't hold if you don't assume excluded middle. Although it already holds if you adopt weak excluded middle, i.e. excluded middle for statements of negated form.

hmm, yes, this is all very smart but is that woman a scientist of some kind? What does she do exactly?

?si=FeW8ZpBU42EI7Nvq&t=3566

wife of bill ackman

she calls herself a designer. all opinions completely discarded

"using old things to create new things" - neri oxman

this woman is a genius. she deserves more credit for all her work and should be more in the limelight to explain her perspective about all sorts of matters

Yes, this is a valid argument.

But if it’s valid you can use it to prove anything.

If I go to the store today I’ll buy milk

If I but milk either I won’t be alive tomorrow or I didn’t go to the store

Therefore either I won’t be alive tomorrow or I won’t go to the store today

The conclusion means that if it’s true that I’m going to the store today then I must not be alive tomorrow, since it’s true that I’d get milk if I went to the store and true that I’m going to the store today, it must be true that I won’t be alive tomorrow if the argument is valid.

You probably don't know about the paradoxes of material implication so here you go: https://en.wikipedia.org/wiki/Paradoxes_of_material_implication

This is a well known problem with trying to use logical/material as English colloquialism for "if/then". Basically you can't really do that and not run into counter-intuitive situations like the one you're describing. You should do some more research and find out what the experts have to say about it.

I’ve seen that before but I don’t see how that’s the problem here

Can you just explain how my rendering of the argument isn’t the same as the argument

Material implication is paradoxical because it does not have causality built-in. Abstract propositions have nothing to do with temporal/physical continuity and causality. You can set up material implications with all sorts of nonsense and the arguments will be logically valid but semantically nonsensical.

>If I went to the bathroom I’m not alive right now or I didn’t wake up today

You just admitted that you wet the bed, little homosexual boy

Ok so if you pick r to be any true statement then the argument automatically becomes absurd since you have p implies q and q implies not p.

Literally just use your 99iq brain to make sure you're not plugging in nonsense to your logic formulas.

Do you not understand how logic formulas work

Do you not understand how reality works?

Youre a moron, you didnt even understand why what I was saying was wrong so I had to figure out out myself. I learned something new while you assumed you knew everything and so learned nothing. You didn’t even read or comprehend my posts because if you did you could have easily explained why I was wrong. have a nice day.

>Being this butt mad over a freshman class meant to filter PHILOSOPHY MAJORS

ngmi

You’re the one that got filtered moron, I understand the argument better than anyone in this thread because I was the only one who was able to explain my mistake.

Cope and seethe moron

Ah I get it now, the argument also happens to imply not P, so you can’t assert P. I was able to conclude absurd things because I was asserting P. Thanks for not helping at all, buttholes

That just means the premises are inconsistent and then the principle of explosion allows you to to conclude anything. From a contradiction one can conclude anything so if your premises are inconsistent then any conclusion is valid.

>Principle of explosion

I prefer to conclude nothing in case of contradictions

Then you should look into paraconsistent logics: https://en.wikipedia.org/wiki/Paraconsistent_logic

>if i buy milk either I won't be alive tomorrow or I didn't go to the store

but that if-then statement isn't true. Of course you can prove a false conclusion with false premises.

It's vacuously true if he never bought milk

the other anons are overcomplicating the answer.

that's vacuous truth. the implication p -> q just says that if p is true then q also must be true and nothing else.

the only way this statement can be false is if p was true but q wasn't.

if p can never be true then p -> q can never be false no matter what q you have since the only case where the implication can be false can't happen.

Such „paradoxes“ just show the logic is valid, but it doesn’t make any statements about the actual real world values you have introduced and which you try to „calculate“. It means within the axiomatic syste of first order logic, all sentences are semantically (i.e. with respect to the relation between the truth values) correct.

So, is formal logic useless? No. As it happens, nature absolutely follows logic. It literally never deviates. So the conclusions you get 100% reflect reality.

So what’s the dilemma with paradoxes? The fact that it’s not determined (by a formal system) what statements you want to introduce. How pertinent they are.

This is just not formalizable. Suppose I introduce the propositions „Elephants have trunks“, „Mars is red“, „I had breakfast with Obama today“.

You can evaluate them logically, but if they are pertinent arguments to prove some argument about e.g. math is up to the human. You can’t find out the relevance of Obama or elephant anecdotes purely from logic.

I'm a professional mathematician and I don't even understand what the frick that pic is saying.

Never took discrete math before.

No one I know writes proofs like that.

Thanks for making me a quadrillonaire in sacrifice of yourself to up to 1000 years in fourth world conditions whilst you blab about breaking the fine balance of nature through impalable. The suns only going to produce an advantage to me, more so the universe. This is set in stone. You'll cost more to computation. I can't wait for you to suck on that glutty meat for 1000 years.

I don't know who you meant to reply to but please take your medicine

It’s propositional deductive logic. It’s the basis for most mathematics and logical reasoning. It’s usually taught in logic classes, discrete mathematics or computer science to teach programming and decision making. Also, it seems like a lot of morons here never took a proper logic course or studied logic.

There’s something called inductive reasoning, Hume literally set treatises on this to correct Aristotelian deductive logic. It’s really just inductive deals with probable truths and is measured as weak and strong, while deductive uses absolute values. It’s not complicated if you’re above 100IQ and can think abstractly. This is why no one takes us philosophers seriously anymore, mouth breathers my math bro.

t. Philosophy major that focused in mathematics now doing cybersec

So basically scribbling stuff on paper and pretending it models the "laws of thinking"

Well no, it just means that there’s propositions or arguments that aren’t based on a true or false statement. I highly suggest you look more into it outside of this thread and board to begin with. I suggest starting light and learning critical thinking, then move on to analogies and fallacies of inductive logic. It’ll help you dissect information much better as well as conveying it. Consider this

>if P then Q

>and Q is S

>then P is S

This argument can only work if all statements are true and absolute, correct?

Well not really, because if P doesn’t have strong evidence to become S then that means it needs enough premises or proof to prove that it is indeed a true statement or rather a strong valid and true statement. This why the inductive logical argument comes in into place. To find inductive validity you need to make decisions and logical proofs based on factors that would render you to come to the conclusion. This includes things like statistical models, past history or the resemblance of analogies.

So to reiterate once again, what I mentioned earlier

>deductive logic is to deal with absolutes

>inductive logic is to deal with flexible or unknown truths that are based on external factors

Both logic techniques are valid and should be utilized depending on the premise, challenge or argument given. So if you’re investigating the cause of a crime then maybe you’d want to use deductive logic, if you’re the lawyer defending the detective for use of force then you use inductive techniques. It’s not just shit on a paper and figuring out what happens.

>I highly suggest you look more into it outside of this thread and board to begin with. I suggest starting light and learning critical thinking, then move on to analogies and fallacies of inductive logic. It’ll help you dissect information much better as well as conveying it.

Shut up you pseud the problem comes from a traditional discrete math textbook and it just used as a structure to prove mathematical statement. It has nothing to do with whatever philosophical blaberring you're on.

I feel sorry for your parents for having birth such an ignorant fricking moron.

>There's propositions that aren't based on a true or false statement

It seems to me like you just contradicted yourself

>Inductive logic

That's a word tool. Not a probability thing. It's about inferring consistency.

>I'm a professional mathematician and I don't even understand what the frick that pic is saying.

It's useful in computer science and engineering. For example you use this kind of logic to design circuits. It is also the basis for certain programming languages such as prolog

>Should I drop the subject altogether?

If you took a "Math" course, but they offer an equivalent "Applied Mathematics" course, then drop it and switch. Presuming the switch isn't accompanied by a large drop in professor quality.

Pure math courses often get too far up their own ass with theory and niche symbol usage.

Finite Mathematical Structures was my favorite "coloring and counting" class.

If p implies q, and q implies either not-r or not-p, then p implies not-r.

The statement p implies not-r is equivalent to the statement not-p or not-r.

Hence, the argument is valid.

What you are basically saying here is:

q - > (~r v ~p)

|= q - > ~r

p - > q

|= p -> ~r

|= ~p v ~r

The trouble is that this is not a valid inference:

q - > (~r v ~p)

|= q - > ~r

This is like saying "if it is sunny outside then it is either not Wednesday or not Tuesday" implies that "if it is sunny outside then it is not Tuesday".

This is false, it could be Tuesday but not Wednesday and the statement "it is not Tuesday or not Wednesday" would be true.

The argument is valid, but your proof is not.

He is 100% correct. He uses modus ponens to say that p implies (~r v ~p), the reformulates the implication into an equivalent disjunction of the form not p or q. Then you use commutativity and associativity to eliminate an extra not p and you end up with the statement ~r v ~p. This is just basic propositional calculus, closer to math than to logic to be honest.

The argument is valid in OP's picrel, and so is your proof of it, but the post I replied to does not prove it the way you do and he makes an invalid inference.

A bad proof does not invalidate a true proposition, it only fails to prove it.

Transitivity.

p -> q

q -> (~r v ~p)

(q->~r) v (q->~p)

p->~r) v (p->~p)

The (p -> ~p) is always false, so you only need to consider p -> ~r, which is a perfectly valid statement.

To go with your example, the actual statement the Op is making is: "If it is Tuesday outside then it is either not Wednesday or it is not Tuesday". Which is a odd thing to say, but logically reasonable.

This is all really cool and I'm really interested but how would I apply to this something practical, say video game design? Would I just represent a game mechanic in math to flex?

Idk most course-level math is basically you either get it or you don't. The ability to do real university-level math well is essentially a weird genetic quirk unnatural to most of humanity (and not particularly special imo). If you need it to finish your computer science degree or something then stick with it, if you are wanting to become a mathematician and you are struggling with pic related then consider changing majors.

Agreed stuff in OPs picrel is literally the first exercice from the first chapter of the first course a math major takes and it's very easy since it only uses the definition of a modus ponens and implications expressed as disjunctions. This is first month stuff

>"""discrete""" """"math""""

>look inside

>logic theory

bruh where did number theory go? set theory? graph theory????

Propositional calculus is literally just the first chapter of a discrete math class to introduce inference rules and proof methods. Set theory is chapter 2. Combinatorics and graph theory are just a little bit later.

>graph theory

>induction

>recursion

>combinatorics

>relations

>basic group theory

>modular arithmetic

>formal languages

those are a part of discrete math and the underlying definitions always have sets. in fact logic itself is defined in term of sets. propositional logic is just a set of logic symbols, a set of propositions and a semantics function (also just a set)

>in fact logic itself is defined in term of sets.

>propositional logic is just a set of logic symbols, a set of propositions and a semantics function (also just a set)

>t. least deranged set theorist

Time for your medication

go ahead, try to rigorously define it without sets

ok so you do the same thing but with words, dumbass.

Sets are merely grammatic-symbolic organizing tools.

Embarrassing how you propped up your fake religion over it.

Everything is a set.

>le deadly paradox incoming

>ok so you do the same thing but with words

Not true

>grammatic-symbolic organizing tools

this his has to be the most pseud way to describe sets. also wrong

>Embarrassing how you propped up your fake religion over it.

if set theory is religio then all math is.

there is a reason everything is defined in terms of sets.

i challenged you to do otherwise but you failed to do so

i must say that you can define math in terms of logic but this is less rigorous and often problematic as logic is too broad

>there is a reason everything is defined in terms of sets.

it's not though you utter brain dead moron

combine p -> q and q -> (~r v ~p) into p -> (~r v ~p)

a -> b is equivalent to ~a v b, so p -> (~r v ~p) can be rewritten ~p v ~r v ~p which is ~r v ~p, so yes it's valid

Yes, transitivity, then reduction

this is much simpler than whatever is going on in the OP.

Solving is just substituting. It's not difficult if you practice.

Its ez. Only hard parts are proofs if you never been exposed to them. A lot of people find inductive proofs in particular difficult and its maybe one of the few ideas on a typical 1st discrete math course that can seem unintuitive, at least in application. The idea itself not too tricky, i like the ladder analogy. But yeah, it can take some practice to see how to actually set up and write an inductive proof correctly.

The rest is mostly counting, relations, graphs, trees, basic logical inferences, modular arithmetic and equivalence classes. All ideas which are readily understood and intuitive.

where do things start to get so unintuitive that your brain needs to be differently wired to understand them?

Idk. Analysis maybe. Linear algebra is pretty well behaved. Discrete most topics are imo more or less intuitive. The continum is where things start getting weird. Algebra and groups/rings etc also gets pretty abstract and I don't think everyone is wired to reasoning with particularly abstract concepts. There's topology too but i couldn't say much about that

Logic and math is rigorous. There's nothing wrong with you if you're having trouble with it.

The derivations in this thread are all correct, but it's still icky because it's so non-constructive. Hence "paradoxes of material implications" are abound with this statement.

A crucial step in the derivation is

[q (a ∨ b)] [(q a) ∨ (q b)]

but this is a form of independence of premise.

For example, let a be the statement "my theory is consistent" and b be the statement "my theory is inconsistent".

Neither a nor b have a prove in your theory, by Gödel.

Let q be just true.

Then a ∨ b says "my theory is consistent or inconsistent" and that's true by excluded middle. So [q (a ∨ b)] is also true.

Now [(q a) ∨ (q b)] is also classically true, but it has nothing to do with two implications anymore. It's "true only formally".

Now say we gent that

[p (not r ∨ not p)] [(p not r) ∨ (p not p)]

Then it indeed follows that

(p not r)

holds.

In turn, it holds that

((not not p) not r)

Now in OP's post we want to arrive at

(not r ∨ not p)

To get there, we must also accept that

((not not p) ∨ not p)

I.e. weak excluded middle for p.

r.i.p.,

it didn't take the nicely formatted arrows, ->

Sorry for being unreadable

>t. am i a midwit?

very possible

maybe study a bit more? discrete math is not remotely hard but it is also not calculus. you can't just do a few problems a section then show up to exams and get an A. you have to study a tad bit more

>how hard is something i didn't learn?

very.

be ready to fail big time i mean not even one correct answer

insanely easy, however if you literally only attended the final then that's your fault for failing.

I actually did get the minimum passing grade but only because 2 out of 4 problems were piss easy, designed for lazyhomosexuals like me so they don't have to see my ugly ass show up again and again

thanks for the perspective. i always had this stupid idea that if i can't learn a semester's worth of content in a day or two or if i don't get everything right away in a given topic i'm not cut out for it, so i always did the bare minimum to pass, i.e. study just enough to get a basic understanding and extensive use of cheat sheets

when is the conscientiousness pill coming out?