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#1 Re: Help Me ! » Big-O and Big-Theta? » 2008-07-23 03:22:53

miche

Then for Big Theta, the only real example I have is:

Show

And I know the answer is:

But I have no idea how the book got to that answer.

#2 Re: Help Me ! » Big-O and Big-Theta? » 2008-07-23 03:12:35

miche

Ok, here's another example that's fairly straightforward...

Show

I know the answer is:

But I don't know how to get to the answer. This is one of the problems in the book where they just give you the answer in the back so i don't know the steps to get there.

#3 Help Me ! » Big-O and Big-Theta? » 2008-07-22 20:30:08

miche
Replies: 23

Hi folks, me again. yikes

I'm having problems with Big-O and Big-Theta notation in general. I don't understand how to find the Big-O or Big-Theta notation of anything, partially because I don't see where K comes in.

To elaborate, I know that...
f(n) is O(g(n))
if
f(n) <= C * g(n) for n >= some k

But if, for example:
7n^2 + 1 is O(n^2)

my answer is:
7n^2 + n <= 8n^2

But I don't see how I got to that point. (This was the only example we had in class and the book is not helpful, it's skipping too much. what )

First of all, what in the world do I do with K?
Second, why do I change +1 to +n in my example?
Lastly... why was 8 chosen?

I'm (as you can tell) quite confused on this. We didn't spend much time on it at all but he suddenly decided to make a big deal about it for the exam. I think he assumes we know it from a previous class, which isn't the case for me. hmm

Any help on Big-O or Big-Theta would be great, truly!

Thank you for reading this,
-Miche

#4 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-22 20:26:19

miche

Hmm.. I kind of understand this a little better then.
I think I need to find more examples to practice on though. I ran out in my book (there weren't many). sad
I'm still not sure on the transitive part, it just isn't sitting well. I can see what you mean, and I can work with that, but I'm not sure I can apply it to more difficult problems (not just a, b, c sort of things... )

Thank you both for your helpful answers. I'm going to try to find some more exercises to practice on then! smile

#5 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-20 18:55:37

miche

Sorry for the triple post. Trying to keep this all in order as much as possible.

For a)
I went through each element until I found one that was not transitive. I am trying to put this in a logic statement since you were talking about it, but I'm not sure if I got this correct.

Here's what I did.

element (1,3)
1R3 ^ 3R3 -> 3R1   Yes (3,1) is present
1R3 ^ 3R1 -> 1R1   Yes (1,1) is present

element (3,3)
3R3 ^ 3R1 -> 1R3   Yes, (1,3) is present

element (3,1)
3R1 ^ 1R1 -> 1R3   Yes, (1,3) is present

element (2,2)
2R2 ^ 2R3 -> 3R2   No, (3,2) is not present so this is not a transitive example

And I stopped there.

So then in this case, I need to have my two antecedent elements provided in my Set, such as 2R2 and 2R3 from the last one.

Then my conclusion (3r2) in that case, is based entirely upon what I already have.

If I do not have the conclusion, then the statement is not transitive. I must check every element in the set, and if any of them are not transitive, then I do not have a transitive statement.

is this correct?

#6 Re: Introductions » Hi - Discrete Math student here... » 2008-07-20 18:35:54

miche

Thanks John E Franklin and mathsyperson. smile
I posted in the Help Me section, so we'll see how it goes.
So far I feel even more confused. Pretty much I'm going to decide by Wednesday whether I will give up. I have never had so much difficulty with a class... calc 2, fine, chemistry 2, fine, astronomy with calc, fine. This class? Killing me. Sigh.

#7 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-20 18:15:22

miche
Ricky wrote:

b. R: yes, the rest are no

I'm assuming you're taking a course in discrete math (or maybe intro to proofs?  Much more likely to be discrete though.) and you've gone over some basic logic fundamentals.  Particularly, you should know what "vacuously true" means.  Let me know if you don't.  In short, all answers to this one are yes.

(And on another note, I should have looked at all of the problems, because this is precisely what I meant by a "trivial" equivalence relation in my previous post.)

d. all are no

Why is this one not transitive?

I assume when you say trivial, you mean something obvious and not masked in a predicate, like X >= Y instead of 3 = 3... is that what you mean?

Well I said d is not transitive because it doesn't work for each node..

Like if you look at 1, 1 is related to 2 (1R2) and 2 is related to 3, (2R3), and 1 is related to 3, (1R3) so that is definitely transitive.

But if you look at node 2, 2 is related to 3 (2R3) but 3 is not related to anything; things are related to 3. So it cannot be transitive because there is no 3R1 or 3R3 or anything like that.

How badly am I messing up here? hmm

#8 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-20 18:09:13

miche

Hi Ricky,

Thank you for your thorough explanation. I am still working through these problems, but somehow something isn't sitting well. I don't know what 'vacuously true' means, though, we never covered it and it's not in our text. I'm in discrete math, by the way. faint

I assume you mean something like where the antecedent of a statement like A -> B is false, then B must be true. But I don't really see how to apply that to this..

I'm sorry, I was making digraphs for these, and that's why I established my answers as such. I'm trying to attach them again, so hopefully this time it works.

I figured that if each node has a self-loop, it's reflexive, if each node has a trip and return trip then it's symmetric, and if there's a short-cut for each node from a trip then it's transitive.. what

#9 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-18 03:28:39

miche

So here's what I think, aside from Antisymmetric, which I still don't quite understand.

a. R: yes, S: no, T: no
b. R: yes, the rest are no
c. all are no
d. all are no

I am trying to attach an image of the digraphs I made for them but I can't seem to attach an image to this post. I select 3 slots and it doesn't bring any up... I'll have to try again after class.

As I understand it, each property must be true for ALL elements in p. Right?

#10 Re: Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-18 02:39:56

miche

Hi Ricky, thanks for your help!

So for transitivity, since 1 is related to 2 (1,2) and there's (2,3) there is also (1,3) so that's yes, but if (1,3) wasn't on the list, would it still be transitive? So then (3,1) & (1,2) & (2,3) is transitive... etc.

But does this have to be true for all elements in p? Because if so, this would not be transitive since (1,3) (3,2) *<--does not exist in p, and (2,3) would be needed, right? Or does just one case for positive transitivity need to be made?

And anti-symmetry... Would the reflexives matter in this? -If something is reflexive, is it automatically antisymmetric? Because 3R3 and 3R3 so then clearly 3=3... or does it have to be two different elements? How can it be antisymmetric without it being also reflexive in this kind of example (as opposed to one that's like x p y <--> x <= y  )?

#11 Help Me ! » Testing for Reflexivity, Symmetry, Transitivity and Anti-Symmetry » 2008-07-17 16:14:52

miche
Replies: 11

Hi guys. Question here with Relations in Discrete Math. I really need to know how to do these, and I would truly love to have a step-by-step method of looking at this kind of stuff:

Let S = {1,2,3}
Test the following binary relations on S for Reflexivity, Symmetry, Transitivity and Antisymmetry.

a. p = { (1,3), (3,3), (3,1), (2,2), (2,3), (1,1), (1,2) }
b. p = { (1.1), (3,3), (2,2) }
c. p = { (1,1), (1,2), (2,3), (3,1), (1,3) }
d. p = { (1,1), (1,2), (2,3), 1,3) }

I have dozens of these kinds of problems, but I don't know what the process is for determining the answers. This is the entire question for one of my problems, but I don't see a relation defined. How do I determine a relation to begin with? Once I have the relation, how do I test for each of the properties? We just skimmed this in class, and so I am pretty well lost!

Any help would be greatly appreciated!

Thank you for reading this.
-Miche

#12 Introductions » Hi - Discrete Math student here... » 2008-07-15 20:24:54

miche
Replies: 3

Hi all,

I'm not especially fantastic at math, but I'm also not especially a poor math student either. I usually make B's, and my favorite math subjects were Geometry and Trig. I took calculus II (B) and astronomy with calculus (A) and physics with calculus (B), I'm decent in math... or I'd like to think so.

However, I'm taking a Discrete math course this summer, and the only thing that I've succeeded at doing in this class is making myself feel terrible. I've continually lost confidence in my math skills and that's only eroding my general confidence, and I've no one to turn to.

My professor's method of teaching is not at all conducive to the way I learn; he rarely answers questions, never goes over homework or quizzes until after the exam, and on top of that, he singles out students (sometimes in pairs) and asks them questions to do at the board. I find this highly intimidating and embarrassing.

Many of the students in my class have done this course in the past and are trying to improve their grades. I've not had this course before, so this is all new to me.  I study for literally 5+ hours a day nearly every day, up to 10 hour before a quiz and more for an exam, and I am only borderline passing. He gives no partial credit and there's no curve. My book does not have enough examples with answers, so I never know if I'm doing anything correctly. There are no summer tutors at campus.

I'm sorry for the sob story, and I'm sure it's not that interesting... The reason why I said all of this is partially because I want to give you a background about my math experience, but it's also because, well, I have no one else to talk to who even knows what Discrete math is.

Thanks for reading this,
-Miche

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