[RESOLVED] Assistance wanted in subject of "Discrete Mathematics"

[freeze_sr]

I need some major help with a few of my assignment questions for the subject of Discrete Mathematics". I tried to google but got all kinds of weird functions and unrelated topics, etc. There are 2 questions here, and i don't understand either.

Can anyone tell me where do i start and how do i go about it? Or a link to something that show examples or how to solve these kind of questions.

[NickThissen]

Are you sure you gave us the right questions? Both of them don't make much sense to me... Maybe it's something to do with the discrete mathematics you mention (never heard of that term before) but I can't see any solution.

For the first, the question asks to verify an inequality, and it shows you an equality, which does not hold.

The second does not seem to hold for any number, let alone an odd integer...?
(replacing lambda with x so I can type it easier):

(x-1)/2 * (x+1)/2 = (x² - 1)/4

So the equation becomes:
x²/4 = (x² - 1)/4
x² = x² - 1

This does not hold for any number as far as I can tell...

[jemidiah]

I think the first question should be "prove that 2n+1 <= 2ⁿ for n >= 3 using induction."

Do you know how to use induction? It's a very important proof technique in discrete math, so I'd definitely recommend getting comfortable with it. Do you want hints on how to do this particular induction (which isn't too tricky, luckily) or induction in general?


I'd have to agree with Nick that the second one doesn't make much sense, since no lambda solve that equation. I guess the statement "all lambda that satisfy equation two are odd integers" is vacuously true but I doubt that's what the question is going for.

[freeze_sr]

So you guys too think theres something wrong here?
I took a screenshot of the question, so no typo on my part.

I've got another question that doesn't make sense, it just simply says this:

Write an algorithm to find unrepeated values

What do they want?

Jemidiah,
If you could get the answer for the original question then please post. If its the modified question, then i might have to ask the lecturer if the question is supposed to be what you said it could be.

[jemidiah]

It sounds like the lecturer isn't terribly careful with the assignments they're handing out.... I could guess that the algorithm question you posted might mean to write pseudocode for a function that takes in a list of numbers as an array and outputs another array with only the unrepeated numbers from the original array, but that's a complete shot in the dark.

As for the first question, I'm virtually certain the "=" sign should simply be a "<="; it makes perfect sense then, and induction is exactly what should be used to prove the modified statement. If you want I'd be happy to walk you through the inductive proof of the modified statement. The second question just doesn't work at all. I believe you'd have to redefine multiplication of integers for it to work out, which is insane.

[freeze_sr]

Thanks for your help, but let me check with the lecturer first before you take the trouble to do the question.
I'll get back to you in 2 days time.

How about this question is this incomplete or there is a solution?

Write an algorithm to find unrepeated values

[NickThissen]

That is hardly a question... You could give an answer of:
y = x

That gives you 1, 2, 3, 4, 5, which are unrepeated values... Somehow I doubt that's what they want

[freeze_sr]

OK, according to my lecturer, the first question is correct.
The question requires me to prove that it is wrong.

The second question had a missing word and should read
" Show that if lambda is an odd integer"

Could you help me out?

[NickThissen]

The first question, as you posted it, does not make much sense.
It shows you an equality and then asks you to verify the inequality..?

Do you need to prove that the expression is NOT valid for every n = 3,4,5...?


The second question is still wrong. The relation you posted does not hold for any lambda, so it does not hold for odd integers either.

[zaza]

Probably it's another inequality posing as an equality...

[freeze_sr]

I was told to give examples for a few. So i assume n=3, n=4 and n=5

[jemidiah]

For the first question, you can show that equality does not hold directly and very easy, as I'm sure you've done by now. The second question still doesn't make any sense, since the equation is never satisfied. Something has to be missing or incorrect.

I'm not terribly impressed with this lecturer from the little I've heard about him in this thread.... It's pretty obvious these questions aren't carefully formed, and his extra explanations at the least weren't very helpful to you.

If you're only supposed to give a few examples of equality not holding for #1, why did he bother to mention induction? I don't get it. If you do the substitution I'm almost certain he's going for for #2, everything simplifies nicely, yes, but the equality *still* doesn't hold.

[freeze_sr]

The lecturer is a she, and apparently the questions were set by the main college and that lecturer that set it is no more with the college. Some great story going on.

For question 1, i'm going to do it just like this

if n=3
2(3)+1 = 2^3
7=8

inequality proven

Then move on to n=4 and so on

For question 2, (show if lambda is an odd integer) the only way i can think of is as following:
(L = lambda)

if L=3, (3^2)/4 = 2.25
          (3-1)/2 = 1
          (3+1)/2 = 2
              2.25 = 2
It has been proven that L is not an odd integer

But then again if I use even numbers it isn't equal either.

I guess this will have to do. I will mark this thread as resolved in a few days time, if there are no better

[jemidiah]

It's unsatisfying to me, but I don't know what the college expects with questions like those. Eh, good luck with the rest of the course . If you happen to find out what the questions meant I'd like to hear it.