Math Problem, Arguement with the teacher. Easy Logic.

[Hiikuro]

As far as I understand, this is logical 'implication', or A -> B.

T -> T = T
T -> F = F
F -> T = T
F -> F = T

Where T and F are true and false. In your example, it means that there is a causal link between taking medicine and feeling better. I guess your teacher tried to explain implication using language, which in my opinion is way too vague to suit such a task.

 

[Singletap]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

I have not heard of Proof By Induction and until I fully comprehend Proof By Inductions I can't tell you rather I agree or not.

Proof's by Induction
Well I don't fully understand the concept either, but basically it's when you prove that something is true simply by assuming so to begin with. Once you've assumed it is true for one thing, you can prove it's true for everything (Sort of)
The first assumption has a reason, but no real justification, you just want it to be true so you say that it probably is. So, even though I've not really solved your problem, I hope to show you that you can assume all sorts of stuff when it comes to these things

But hey, I'm not a Maths teacher, just a student!

Right that does help, so you assume not to get a answer but just to check if your assumption is correct so you can then proceed to the answer and then you can tell if your guess was right or wrong.

That would work the only problem is that we don't have an extended question that you can do that with, the if then is the question.

 

[Tallim]

Think of it as a drinking game and the true or false is dependant on if you follow the rules.

If you see a camel then take a drink. (stupid but whatever)

So if you see a camel then take a drink - you have followed the rules so true.
if you see a camel then don't take a drink - you have broken the rules so false.
if you don't see a camel then take a drink - tricky one but you haven't broken the rules: true.
if you don't see a camel then don't take a drink - you have followed the rules so true.


I don't much like the wording your teacher used. But she is correct.

I'm sorry I don't understand, If I see a camel then I take a drink right, well why would I take a drink if I didn't see the camel, what if the drink is acid I don't want, that so I choose not to take a drink because I didn't see the camel.

Ok you are either failing completely to see that the circumstances don't matter at all in the statements. I could use: If A then B, and the arguments would be the same.

Or you are an elaborate troll of some kind.

 

[TWRule]

Here's how it works with conditionals:

1) If (True) then (True) = The statement as a whole is True
2) If (True) then (False) = The statement as a whole is False
3) If (False) then (True) = True
4) If (False) then (False) = True

This is because when you're evaluating the truth of the whole statement, all that matters is whether the first term will necessarily cause the second term.

The reason number 2 is false is because you're trying to prove a connection between two things that might not actually be there. You cannot take your medicine without feeling better.

Number 3 is true because you can not take the medicine and still feel better, and 4 is true because it's also possible that you will not take the medicine and not feel better because of it (it's just a reverse of number 1).

I don't know if your teacher taught you necessary and sufficient conditions, but generally the first term is a sufficient condition for the second but not a necessary one, while the second term is necessary for the first but not sufficient.

What this means is: It is impossible for you to take your medicine and NOT feel better (as this particular statement is claiming - which you have to assume is true). But taking your medicine alone isn't necessarily enough to make you feel better - you'll probably also need rest and fluids, etc.

 

[Drug Crazed]

This is a real ***** to understand. The way to think on it is it doesn't say what happens if A is false.

Itsan implication, for which the truth table is
A B A=>B
T T T
T F F
F T T
F F T

So, the way I like to say is, if A is true, then B has to be true. Otherwise, we have a contridiction. However, we don't know the affect of not A on B, so we assume it to be true regardless.

 

[Mike Laserbeam]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

I have not heard of Proof By Induction and until I fully comprehend Proof By Inductions I can't tell you rather I agree or not.

Proof's by Induction
Well I don't fully understand the concept either, but basically it's when you prove that something is true simply by assuming so to begin with. Once you've assumed it is true for one thing, you can prove it's true for everything (Sort of)
The first assumption has a reason, but no real justification, you just want it to be true so you say that it probably is. So, even though I've not really solved your problem, I hope to show you that you can assume all sorts of stuff when it comes to these things

But hey, I'm not a Maths teacher, just a student!

Right that does help, so you assume not to get a answer but just to check if your assumption is correct so you can then proceed to the answer and then you can tell if your guess was right or wrong.

That would work the only problem is that we don't have an extended question that you can do that with, the if then is the question.

That's pretty much it yeah
Except you find your answer by using another assumption, it get's more complicated but you basically get it
But you're right, in this situation, there's nothing you could really use it for!

 

[demoman_chaos]

Once I was asked to find X, so I circled the X and drew an arrow. The teacher gave me credit on the question since I did find X as I was asked, but was quite displeased and said to not do it again.

 

[microwaviblerabbit]

Ever heard of Proof By Induction?
First Step:
Assume true for n=1

Maths is all about assumption

I have not heard of Proof By Induction and until I fully comprehend Proof By Inductions I can't tell you rather I agree or not.

Proof's by Induction
Well I don't fully understand the concept either, but basically it's when you prove that something is true simply by assuming so to begin with. Once you've assumed it is true for one thing, you can prove it's true for everything (Sort of)
The first assumption has a reason, but no real justification, you just want it to be true so you say that it probably is. So, even though I've not really solved your problem, I hope to show you that you can assume all sorts of stuff when it comes to these things

But hey, I'm not a Maths teacher, just a student!

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.

 

[Darth IB]

Right, the teacher said the same thing, innocent until proven guilty but I don't see why I should consider it as innocent, I don't know that why not just say I don't know. It's more correct it seems to me. If I see someone in court and he is being accused of committing a crime I don't say, that man is innocent! I say I hope that man is innocent but I don't know that.

But if there's nothing suggesting he's guilty, accusing him seems rather strange, no?

As for logic, adding a variable other than "True" and "False" will only serve to make things complicated. "Don't know/Can't say/Maybe" will get you nowhere when trying to prove something (on this level). Such things are present in more advanced logic however - Quantitative Logic for instance has a system for "For all X" and "for some X" which allows for some variants of uncertainty. But Propositional Logic keeps it basic.

 

[Drug Crazed]

Right, I'm seeing fallacies in induction so I'm going to explain. It works like this.

I'm trying to prove x for all n.
Let us see if x works if n=1. I show that it does.
Then I assume x works for n=k. I then show that using that assumption, I can prove x works for n=k+1.
Thus, I say for any n, n+1 works. As I know n=1 works, I know n=2 works. If n=2 works, n=3 works etc.

And now I can say I've done MAS105 revision.

 

[Sonic Doctor]

Hello Escapist Forum

Today me and my tenth grade geometry teacher had a argument. I'm not great in math class but we recently started logic and it seems to come very easily to me, most likely through making games and such on the computer.

Here is the problem and I don't see the logic in her teachings.

We were going over the "If" "Then" statements and one of the problems was.

If you take your medicine then you will feel better

we then had to take the 4 truth or false cases and decide rather they are true or false, easy right?

Well I had a small problem with case 3 and 4, they said

"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"

She said they default as true, I argued that that's impossible, they must be undefined, I see no truth in these cases you can't just assume in math without a reason to.

She got very worked up thinking that I was trying to confuse the kids but I simply did not understand the logic and she didn't make a good attempt to show me what she was saying. I'm still confused and I believe she is wrong I will change my thoughts if I can see a sense of reason.

Can I get some help here.

From Jesse Bergerstock aka SingleTap "Tap"

What the heck are you kids doing in schools these days. I never had to do this stuff in any math class ever.

In my geometry class, we learned something I like to call....geometry. You know, the thing that involves shapes and angles and all that Greek. If what you are learning was in our books at that time, I can tell you why it wasn't taught, it isn't used in anything in the future and it doesn't sound like productive work.

I don't know what your school thinks it is doing, because the stuff you are doing isn't going to prepare you for college, I took a couple college level math classes that involved geometry, and they didn't involve that stuff. It doesn't even resemble geometry.

Though if I was going to guess, my thought being that the person involved with the question is sick, then I would see "If you don't take your medicine then you won't feel better" as being right. But really since there are so many unforeseen variables, you can't really answer any question like this, nothing is right and nothing is wrong. So it is pointless.

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.

 

[Singletap]

This is a real ***** to understand. The way to think on it is it doesn't say what happens if A is false.

Itsan implication, for which the truth table is
A B A=>B
T T T
T F F
F T T
F F T

So, the way I like to say is, if A is true, then B has to be true. Otherwise, we have a contridiction. However, we don't know the affect of not A on B, so we assume it to be true regardless.

So we don't assume it to be true for laughs and giggles we assume it to be true because there is no problem with the math that it uses?

 

[Drug Crazed]

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.

 

[Liquid Paradox]

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?

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.

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.

Chin up, though: if you get into a good College or University, where teachers are paid to take their students seriously, things will change. for now, the best thing you can do for yourself is learn to do whatever the idiot at the front of the class tells you to do (within reason, of course).

 

[TWRule]

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.

 

[HarmanSmith]

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.

 

[Singletap]

Hello Escapist Forum

Today me and my tenth grade geometry teacher had a argument. I'm not great in math class but we recently started logic and it seems to come very easily to me, most likely through making games and such on the computer.

Here is the problem and I don't see the logic in her teachings.

We were going over the "If" "Then" statements and one of the problems was.

If you take your medicine then you will feel better

we then had to take the 4 truth or false cases and decide rather they are true or false, easy right?

Well I had a small problem with case 3 and 4, they said

"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"

She said they default as true, I argued that that's impossible, they must be undefined, I see no truth in these cases you can't just assume in math without a reason to.

She got very worked up thinking that I was trying to confuse the kids but I simply did not understand the logic and she didn't make a good attempt to show me what she was saying. I'm still confused and I believe she is wrong I will change my thoughts if I can see a sense of reason.

Can I get some help here.

From Jesse Bergerstock aka SingleTap "Tap"

What the heck are you kids doing in schools these days. I never had to do this stuff in any math class ever.

In my geometry class, we learned something I like to call....geometry. You know, the thing that involves shapes and angles and all that Greek. If what you are learning was in our books at that time, I can tell you why it wasn't taught, it isn't used in anything in the future and it doesn't sound like productive work.

I don't know what your school thinks it is doing, because the stuff you are doing isn't going to prepare you for college, I took a couple college level math classes that involved geometry, and they didn't involve that stuff. It doesn't even resemble geometry.

Though if I was going to guess, my thought being that the person involved with the question is sick, then I would see "If you don't take your medicine then you won't feel better" as being right. But really since there are so many unforeseen variables, you can't really answer any question like this, nothing is right and nothing is wrong. So it is pointless.

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.

Logic is used in programing and thought processing as far as I can see. I've used if then statements and the sort with Java programing.

 

[Kezboard]

That's pretty much it yeah
Except you find your answer by using another assumption, it get's more complicated but you basically get it
But you're right, in this situation, there's nothing you could really use it for!

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)

 

[inFAMOUSCowZ]

I hated these last year/ They were easy as hell, but made no sense. One could be false, and the other could be true, and then the whole statement could be true. Stupid in my opinion, also I'm guessing your in geometry, if your doing these. Just wait until you have to prove something is a triangle, or a circle. Fun stuff /sarcasm.