Math Problem, Arguement with the teacher. Easy Logic.

[Drug Crazed]

ok, so in this problem, you are supposed to assume that the statement "if you take your medicine, then you will feel better" is the truth?

if that is the case...

"if you don't take your medicine, then you will feel better" must be false.

Consider the following key (or legend):
"If you [do]"* is positive, or 0 + x (where x is medicine)
"Medicine" = 5
"then" is equal to, or =
"will" is also positive, or +
"if you don't" is negative, or 0 - x (still medicine)
"you won't" is also negative, or -
"feel better" = 5

still with me?

That isn't how logic works!

The term "if you don't" is the opposite of "if you [do]". so, lets look at it like this: "if you don't take your medicine (0 - 5), then (=) you will (+) feel better (5). 0 - 5 equals -5, therefore the statement 0 - 5 = 5 is false.

Using the same logic, the statement. "If you take your medicine, then you will not feel better" is also false. if "you will" is positive, then "you will not" is negative. so, "If you [do] take your medicine (0 + 5) then (=) you will not feel better. [-5]" however, since 0 + 5 =/= -5, that statement is false.

The problem is that the statement "If you take your medicine, you will feel better" only tells you about what happens if you take your medicine. Thus, you can't say its false, because it might not be. The reason you say its true is because you can't say its false.

I suggest you take your teacher aside and show her this logic, away from the class so that she can't call shenanigans on you. Explain the key to her, and show her why both answers are false. If she is willing to see your point, then good! She is a good teacher who is willing to overlook her pride in order to foster your strength in logic. If not, well... don't despair! the problem with highschool is that a LOT of teachers are needed to fill the millions of classrooms across the United States (or where ever you live) and that means that there is a very low standard for highschool teachers. I.E. she is probably not a very good teacher. (don't tell her that) I could rant for hours about that, but this is already a tl;dr.

The issue here isn't that the teacher is an idiot and teaching the wrong thing. She's teaching the truth. She's just not explaining why it must be true effectively

Wikipedia appears to have the best solution with this referenced: http://www.math.niu.edu/~richard/Math101/implies.pdf

 

[Liquid Paradox]

Thing is, there is no 'undefined' in Formal Logic. "if A then B" is considered to be true as a statement if both A and B are true, or if A is false (regardless of B's truth value). This is because as long as A is not true (e.g. medicine is not taken) it can not be inferred that A does not cause B.

aww crap... this is a conundrum. ...yeah, I think Darth IB might be correct. In my earlier post I was looking at the statement as a direct math problem, not a logic problem. While my equation seems correct to me, it all depends on what is implied by the original statement. I was assuming that both a and b were true. I would have to see the context of the original question before I could answer it.

snip

yes, I was over thinking it as a math problem, not a logic problem

also, I never meant to imply that the teacher was definitely an idiot, I was making a joke based on the idea that some teachers are idiots, especially in highschool, and that it is fruitless to argue with an idiot. For the record, I do not know your math teacher, and thus have no basis of which to tell you that she is an idiot Especially since I now think that she was right, and I was wrong

 

[Lem0nade Inlay]

Logic and Probability (all those things that aren't THAT much to do with maths, but more just logical thinking) can be very confusing, albeit seemingly easy. As with these types of maths assumption is a big part, and unfortunately that's just the way it is.

Your teacher was wrong to get angry at you for it, though. She should have explained it more and listened to what you have to say.

 

[Sonic Doctor]

I recommend you tell your teacher that what she is teaching is stupid, and isn't going to be used anywhere except inside the class. Tell her to actually teach geometry like teachers in other schools do.

Which surprisingly is like an awful lot of geometry. However, if you're going into Computer Science or game development, you'll find this stuff very usely.

Actually, I graduated with a BS in English. And it is useful, usely is not a word.

 

[Shynobee]

If you take your medicine then you will feel better

"If you don't take your medicine then you'll feel better"
"If you don't take your medicine then you won't feel better"

From Jesse Bergerstock aka SingleTap "Tap"

Here are the givens based on the first statement:
medicine makes you feel better
no medicine means you stay sick forever

thus:
case 3 should be false
case 4 should be true

Based on reading what you said, this is how I see it. I assumed the givens based on the initial question.

In math, you make a lot of assumptions. Get used to that one.

What you said can be correct but also it could also be that the medicine ends up not helping at all which could make it false which brings us back to the beginning of it being a %50 %50 shot.

Also I don't understand why you should have to make assumptions in math, they must have been proven before people just started assuming right?

You are making the biggest assumption that the medicine will not help.

What you need to understand is that school math lives in a bubble. The ways of reality and actual life do not apply. You take what is given, and nothing else. In other words, you are reading too deeply into the problem. You can't do that in school math.

 

[Danny Ocean]

The premise is that If you take your medicine then you will feel better.

He doesn't say that you will not feel better if you do not. That is an assumption you are making.

Hence the only known false possibility listed would be 3:

1. You do take your medicine and do feel better. - T
2. You do not take your medicine and do feel better. - T
3. You do take your medicine and do not feel better. - F
4. You do not take your medicine and do not feel better. - T

Because we know that taking medicine makes you feel better.

...Right?

 

[castlewise]

As is so often the case in math, you are both right in some sense. See the thing is that

A->B (shorthand for A implies B) is _defined_ to be true in the following cases:
A True and B True
A False and B True
A False and B False

and false in the case

A True and B False

Its not really a matter for interpretation. Thats how thousands of mathematicians and computer scientists define A->B and you are kind of stuck with their conventions You are correct that it is a little strange for us to say that the statement "If the sun rises in the west then John Funk is a girl" is true just because the "A" part is false. It contradicts your intuition a little. There is a reason however. Suppose we did it as you suggest and define

A-> B to be true in the case:
A True and B True

and false in the cases:
A False and B False
A False and B True
A True and B False

You may recongnize this as exactly the same thing as "A AND B"; it would be true in only the case where both A and B are true. So, unless we want "implies" to be the same thing as "and", we have to define "A->B" to be true when A is false.

Now, this is all under the assumption that we are dealing with computer logic. It makes sense to say that the statement A->B is undefined if A is false. But there is no undefined for computers (or for logic) only true = 1 and false = 0, so you have to pick one.

 

[FarleShadow]

I'm going to agree with your teacher, in the sense that you should just accept it and get on with something else.

Because one kid is not going to change the nature of education, no matter how many 'I R SPECIALZ!' cartoons anyone watches.

 

[Sonic Doctor]

I recommend you tell your teacher that what she is teaching is stupid, and isn't going to be used anywhere except inside the class. Tell her to actually teach geometry like teachers in other schools do.

Teaching basic logic is stupid? It's valuable on it's own, and geometry is derived from logic. It will prepare them for college too, because critical thinking courses are generally required nowadays. I'd taken college courses that teach you exactly what he's learning now - he's better off learning it sooner, if possible. If you don't understand the basics of logical reasoning, the rest of geometry makes no sense - it seems like a collection of arbitrary rules to the student.

I don't know about other students but I never questioned the rules behind the work, and geometry made plenty of sense to me, and I didn't have to learn that logic stuff.

I didn't care for math because it wasn't what I was going to be doing, but why question it when you do it with the rules in mind and get it right. So, I got it right, move onto the next problem.

 

[Singletap]

The premise is that you will feel better if you take your medicine.

He doesn't say that you will not feel better if you do not. That is an assumption you are making.

Hence the only known false possibility would be 3:

1. You do take your medicine and do feel better.
2. You do not take your medicine and do feel better.
3. You do take your medicine and do not feel better.
4. You do not take your medicine and do not feel better.


...Right?

Man this is such a 50 50 shot to me. On one side I see your point that he wasn't wrong but he also wasn't necessarily right.

 

[Singletap]

If you take your medicine then you will feel better

"If you don't take your medicine then you'll feel better"
"If you don't take your medicine then you won't feel better"

From Jesse Bergerstock aka SingleTap "Tap"

Here are the givens based on the first statement:
medicine makes you feel better
no medicine means you stay sick forever

thus:
case 3 should be false
case 4 should be true

Based on reading what you said, this is how I see it. I assumed the givens based on the initial question.

In math, you make a lot of assumptions. Get used to that one.

What you said can be correct but also it could also be that the medicine ends up not helping at all which could make it false which brings us back to the beginning of it being a %50 %50 shot.

Also I don't understand why you should have to make assumptions in math, they must have been proven before people just started assuming right?

You are making the biggest assumption that the medicine will not help.

What you need to understand is that school math lives in a bubble. The ways of reality and actual life do not apply. You take what is given, and nothing else. In other words, you are reading too deeply into the problem. You can't do that in school math.

Why make the biggest assumption that the medicine will help?

 

[Danny Ocean]

Why make the biggest assumption that the medicine will help?

Because that is the premise the whole thing is working on. It is taken as a truth. If you don't make that assumption you're left knowing nothing and so unable to create a truth table like that.

 

[Singletap]

I'm going to agree with your teacher, in the sense that you should just accept it and get on with something else.

Because one kid is not going to change the nature of education, no matter how many 'I R SPECIALZ!' cartoons anyone watches.

I couldn't care less about changing the nature of education, I would like to understand what she is presenting to me. Don't act like I am trying to start a solo revolution because of it.

 

[Singletap]

Why make the biggest assumption that the medicine will help?

Because that is the premise the whole thing is working on. It is taken as a truth. If you don't make that assumption you're left knowing nothing and so unable to create a truth table like that.

Why make the truth table if it could be wrong. What if it ends up being true and it is actually false wouldn't that create a problem in a code?

 

[jojoemon]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

I don't understand how the hole of math is a assumption, I have decided that using mathematics is the best way to determine reality which is the nothing less than the absolute truth of things. How can you assume the truth of something when you could be wrong, this makes it non absolute and pointless to consider as fact.

Also, how can you say that it is true. What if you got worse if you did take the medicine which would make it false. There is a %50 %50 chance there.

Math is all assumtion because we assume that 1 is 1. Ect. It's a system used to describe the world around us; fromt he basic assigned values new ones were derived, with equations and systems becoming incressingly complex. The more complex our mastery of the subject, the more of the world we are able to describe with it.

 

[FarleShadow]

I'm going to agree with your teacher, in the sense that you should just accept it and get on with something else.

Because one kid is not going to change the nature of education, no matter how many 'I R SPECIALZ!' cartoons anyone watches.

I couldn't care less about changing the nature of education, I would like to understand what she is presenting to me. Don't act like I am trying to start a solo revolution because of it.

Speaking as someone who took a 'System design' class at university, I understand that some shit is utterly stupid and difficult to absorb, but you just have to accept that what they teach is correct. This isn't about starting a revolution, its about sitting down with a big bowl of utterly incomprehensible gibberish and very slowly spooning your way through it.

I'm figuring its just a bad example of a stupid system, but if that's what you gotta learn, you gotta learn it. or fail. Your choice.

 

[Kezboard]

Induction itself is flawed when you're in the real world. Take this for example.

A woman is at an airport in Richmond. Her flight to Boston is running late. She sighs and says to herself, "if I were not here, I would be in Boston." Using induction, if the woman were in Alaska, then she would be in Boston.

I'm no stranger to confusing teachers, but logic and induction are inherently, well, wierd.

Actually, you can apply predicate logic to the real world: the woman's statement is false.

Here's my proof:
A := "I am in Richmond"
B := "I am in Boston"
C := "I am in Alaska"

Her claim:

¬A => B
(or in words: If A is false (read "¬" as "not") then B is also true)

Let's assume, that it is impossible to be at two places at the same time, which I don't believe is much of a stretch:

(A xor B xor C) and (A xor C)
(Either A or B or C or neither is true) (xor means "exclusive or")

We observe that C is true, therefor neither A nor B are true:
¬A, ¬B

The claim was, that if A is false, then B must be true. However, B is false, which means that the claim contradicts established facts and is therefor false.

(phew, that took longer than I originaly expected.)

 

[Singletap]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

I don't understand how the hole of math is a assumption, I have decided that using mathematics is the best way to determine reality which is the nothing less than the absolute truth of things. How can you assume the truth of something when you could be wrong, this makes it non absolute and pointless to consider as fact.

Also, how can you say that it is true. What if you got worse if you did take the medicine which would make it false. There is a %50 %50 chance there.

Math is all assumtion because we assume that 1 is 1. Ect. It's a system used to describe the world around us; fromt he basic assigned values new ones were derived, with equations and systems becoming incressingly complex. The more complex our mastery of the subject, the more of the world we are able to describe with it.

If you can prove 1 is 1 then you aren't really assuming then are you?

 

[Mike Laserbeam]

Actually, no.
In fact, you're so wrong, you made me register an account to correct you.

Proof by induction works like this:

You *prove* that your claim is correct for n=1 (or where ever else you start), then you *prove* that, if the claim is correct for n=k, it's also correct for n=k+1 (or some other step size, depending on the problem).

If you combine those two *proven facts* that the claim is correct for all n, since if it's correct for 1 it's also correct for 2. And if it's correct for 2 it's also correct for 3. Imagine, if you will a row of dominoes falling, each one pushing over the one after it.

(Apologies if unclear, not a native speaker)

The first one isn't an assumption, it is the base case. You prove this with normal mathematics. Its usually used to prove formulas to explain mathematical patterns in numbers, so first you work out the first few values of the pattern, then create a formula then use the proof by induction to prove the formula for all values of the pattern.

Right right, basis case n=1, inductive step assume true for n=k, show that true for n=k+1, there's an assumption which was my main point.

 

[YouBecame]

The whole of maths is pretty much assumption.
As is everything.
It could be that you'll get better anyway, so that would be true.

I don't understand how the hole of math is a assumption, I have decided that using mathematics is the best way to determine reality which is the nothing less than the absolute truth of things. How can you assume the truth of something when you could be wrong, this makes it non absolute and pointless to consider as fact.

Theorems are the cornerstone of mathematical discovery and are build upon axiomic truths: Things assumed to be true just because they are obvious. Inct, there have been examples where a convoluted axiom has led to odd mathematics, for example Euclid in his treatise The Elements, assumed something about triangles which can be untrue if you inscribe the triangle on a sphere. Mathematicians like Newton were left assuming that Calculus had some reason to work, just because their methods seemed to give plausable answers. Hundreds of proofs were constructed upon an unproven theory just because they hoped the theory was true.

In essence, you would be surprised jsut how much we assume to know in mathematics.