Math Problem, Arguement with the teacher. Easy Logic.

[TiefBlau]

These are all shitty examples.

All you need to know about geometry-level logic:

"If A, then B." Is the original statement, which you assume to be true.
Then "If B, then A." Would be the converse, which you can't assume to be true.
Furthermore, "If not A, then not B." Would be the inverse, which you also can't assume to be true.
Finally, "If not B, then not A." Would be the contrapositive, which you can logically deduce is true.

Your teacher phails at geometry-level logic by providing statements that are none of the above. To use your statement,

"If take your medicine, then you'll feel better." - Original Statement (Assumed true)
"If you feel better, then you took your medicine." - Converse (Not always true)
"If you don't take your medicine, then you won't feel better." - Inverse (Not always true)
"If you don't feel better, then you didn't take your medicine." - Contrapositive (Definitely true)

Therefore, not only does your teacher introduce a statement that's none of the above ("If you don't take your medicine, then you'll feel better."), but she gets one of the statements wrong ("If you don't take your medicine, then you won't feel better." Isn't always true, since it's an inverse).

 

[TiefBlau]

(double post >.<)

 

[Eric the Orange]

snip

While I may not know the specifics of proofs I can give some advice about student/teacher relations. If you have a disagreement with what is being taught, it's best to say these things in a more solo or private setting, instead of in front of the class.

 

[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.

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.

Well, I'd say your sentiments are quite common; not in that you didn't question how geometry was taught but that you aren't interested in it. Math in general is a rather unpopular subject, and I'd wager that how it's taught has something to do with that. Students generally might find it a lot more interesting if they had such an understanding of it's basis, rather than treating it as merely something that has to be memorized for school. But anyway, sorry for getting off topic.

 

[Count Igor]

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.

Well, Humans invented Maths, and so, as humans are imperfect, we just have to assume that whatever calculations we're using are right, otherwise nothing gets done.
Besides, you CAN get worse if you take the message. I never said you couldn't. I was just rushed for time and barely managed anything.
Think about it. Medicine helps recovery, but isn't 100% effective. People still die. I'm not arguing that.
But, if you got better if you took your medicine, then that doesn't rule out the fact that you can get better if you DIDN'T. They're not mutually exclusive, as both would play a part in it.
What I'm saying is, you seem to be intentionally causing trouble here, as it's a maths lesson, not a philosophy one, and the teacher could have been right.
Hell, you just assumed there was a 50/50 chance of getting better if you did take the medicine. You have no proof to back that up there, so you just did the same thing as the teacher, and assumed.
I don't see the problem here. It's a simple question which has two statements that aren't mutually exclusive. I mean, if I said Red is a colour and Blue is a colour, then you wouldn't argue right? Not even that because Red is a colour then how on EARTH could Blue be a colour AS WELL? I'll tell you. Because they're not mutually exclusive. (Red and Blue can both be colours at the same time)

Also, as a side note, I know Mutually Exclusive term doesn't work too well on the Medicine one, but I couldn't remember the one that did.

 

[Eclectic Dreck]

"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"

The first statement gives us a condition: that we take medication. It gives us a result: that you feel better. This is a coherent and logical statement (we have established a cause and an effect). The second statement does the same thing.

How you interpret these statements will vary greatly. There are three basic interpretations:

1) Each statement is a part of the "rules" governing the logical system. In this case each statement is necessarily true within that rule set.
2) The one statement or the other is part of the rules governing the logical system. In this case, given one rule the second rule is not necessarily true.
3) Neither statement is a rule of the logical system in which case the reader cannot assume either statement is true.

In the first case it is easy enough. These arbitrary rules can be defined as true because the logical statement being made is simply "if A then B". One might be tempted to reason that there is no proof inherent but no such proof is required when one is simply stating an arbitrary connection such as this.

The second case is a hair more complex. Because the statement that is made is "if A then B", and we are given no other information it does not stand to reason that if we do not have A then we would also not have B. A simple change can of course give us this meaning. If we said "You will feel better if and only if you take your medicine" then we would know that if we did not take our medicine we would not feel better as it has been established that the only way to feel better is to take the medicine (the power of the "if and only if" part).

The third case is the way most people would view the statements unless otherwise directed. You establish a connection between the two without any supporting evidence and as such neither statement has value. If I were to simply make the assertion "If you take Viagra you will gain the hidden power of flight", people would expect some supporting evidence.