A Problem - I need help

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You need to show some of your work and say what trouble you are having.
 
pka said:
Please read the guidelines for posting.
You need to show some of your work and say what trouble you are having.
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Okey. I want to find complement Cluster A .

And Cluster A is 6xy+x-y and x,y € Z+
and A' € Z+ too.

And İs Every pattern's complement is pattern too ? For example 3x is a pattern on Z+. So complement is 3x+1 and 3x+2 so its okey. But Does every function provide this?

And my english so bad .Sorry I cant explain myself exactly.
 
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nuret94 said:
A={x,y€Z+ : 6xy+x-y }

A'€ Z+
A' ? (What's comlepement of A )
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Please check that you have stated this problem fully and correctly.

I assume you meant this:

A={ x,y∈Z+ : 6xy+x-y }​
​
A' ∈ Z+​
A' = ?​

But that is meaningless, so something is wrong.

The definition of A says, "A is the set of all pairs of positive integers x, y such that 6xy+x-y". The part following the colon has to be a statement that can be true or false, not an expression with a numerical value. Possibly what you intended was "A={ 6xy+x-y : x,y∈Z+ }", which says, "A is the set of all numbers that can be expressed as 6xy+x-y for positive integers x and y", and amounts to asking for the range of the function z = 6xy+x-y when x and y are restricted to positive integers.

If A is a set, then its complement A' is a set, not an element of the positive integers. Possibly you really meant "A' ⊂ Z+", and intended that to say that the universe within which you are defining the complement consists of the positive integers. In other words, you may be asking which positive integers can't be expressed as 6xy+x-y.

Again, please clarify and check the problem. If you have not quoted exactly the problem as given to you, please do so.
 
Dr.Peterson said:
Please check that you have stated this problem fully and correctly.

I assume you meant this:

A={ x,y∈Z+ : 6xy+x-y }​
​
A' ∈ Z+​
A' = ?​

But that is meaningless, so something is wrong.

The definition of A says, "A is the set of all pairs of positive integers x, y such that 6xy+x-y". The part following the colon has to be a statement that can be true or false, not an expression with a numerical value. Possibly what you intended was "A={ 6xy+x-y : x,y∈Z+ }", which says, "A is the set of all numbers that can be expressed as 6xy+x-y for positive integers x and y", and amounts to asking for the range of the function z = 6xy+x-y when x and y are restricted to positive integers.

If A is a set, then its complement A' is a set, not an element of the positive integers. Possibly you really meant "A' ⊂ Z+", and intended that to say that the universe within which you are defining the complement consists of the positive integers. In other words, you may be asking which positive integers can't be expressed as 6xy+x-y.

Again, please clarify and check the problem. If you have not quoted exactly the problem as given to you, please do so.
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Definitely you are right. I couldn't explain myself sorry . But you understend true me . Thanks for that. And what do you think for tihs question ?
 
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Okay, let's take the problem as being this:

Given A={ 6xy+x-y : x,y∈Z+ }, find its complement in the set Z+.​

(By the way, you might want to convince yourself first that A is in fact a subset of Z+.)

Here is where pka's response comes in: Please show us what you have tried, and where you are stuck, as we request in our guidelines. Among other things, this gives us an idea of what kind of help will be useful to you, by showing us what techniques you are learning, as well as anything you might be doing wrong. Anything you can tell us about what you've learned (for instance, are you in an algebra class, or have you learned some number theory?) will help us to make suggestions appropriate to your own needs.

Also, I asked you to quote the problem exactly as given to you; it is quite possible that, having misstated it once, you are still wrong in claiming that the problem as I have restated it is correct. If it was not presented in the symbolic form you showed, how was it stated?

But, assuming you have not learned any special methods for handling this, I would start by just "playing" with the set. Make a table of values of x and y, and from that make a list of elements of A. That will give you the beginning of a sense of how the set "works". As you do that, you may get an idea of why a number might not be in set A. If you've done nothing else, show me at least the results of that experiment.
 
nuret94 said:
Okey. I want to find complement Cluster A .
And Cluster A is 6xy+x-y and x,y € Z+
and A' € Z+ too.
And İs Every pattern's complement is pattern too ? For example 3x is a pattern on Z+. So complement is 3x+1 and 3x+2 so its okey. But Does every function provide this?
Click to expand...
tablex1.gif Here is a table where x=1 to 15. Like Prof Peterson I urge you to experiment with various values of y. Can you show that \(\displaystyle \;6\in A~?\)
Is it true that \(\displaystyle \;5\in A~?\) Using the table above, if \(\displaystyle x=6~\&~y=2\) then \(\displaystyle \;76\in A~?\)
You can use the link to generate other tables.
 
But I want to find a function - a pattern .
Does A' has a pattern ? İf it has a pattern what it is ?
 
Dr.Peterson said:
Okay, let's take the problem as being this:

Given A={ 6xy+x-y : x,y∈Z+ }, find its complement in the set Z+.​

(By the way, you might want to convince yourself first that A is in fact a subset of Z+.)

Here is where pka's response comes in: Please show us what you have tried, and where you are stuck, as we request in our guidelines. Among other things, this gives us an idea of what kind of help will be useful to you, by showing us what techniques you are learning, as well as anything you might be doing wrong. Anything you can tell us about what you've learned (for instance, are you in an algebra class, or have you learned some number theory?) will help us to make suggestions appropriate to your own needs.

Also, I asked you to quote the problem exactly as given to you; it is quite possible that, having misstated it once, you are still wrong in claiming that the problem as I have restated it is correct. If it was not presented in the symbolic form you showed, how was it stated?

But, assuming you have not learned any special methods for handling this, I would start by just "playing" with the set. Make a table of values of x and y, and from that make a list of elements of A. That will give you the beginning of a sense of how the set "works". As you do that, you may get an idea of why a number might not be in set A. If you've done nothing else, show me at least the results of that experiment.
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İt's only my work. I want to find for A' a function - a pattern . How can I find it?
 
There may be no visible pattern. If there is, it is your task to find it! You must try something, or you will not get anywhere.

Since you still have not quoted the actual problem or told us the context, I have no idea what sort of answer is expected, or what techniques you are expected to use. I can tell you that you can probably expect to be able to identify a largest number in A', but for numbers below that, there may be no simple way to describe the set other than to list its elements.

By the way, the word "function" does not imply a "pattern" in any familiar sense; a function can look entirely random. What sort of function or pattern do you expect, and why?
 
Dr.Peterson said:
There may be no visible pattern. If there is, it is your task to find it! You must try something, or you will not get anywhere.

Since you still have not quoted the actual problem or told us the context, I have no idea what sort of answer is expected, or what techniques you are expected to use. I can tell you that you can probably expect to be able to identify a largest number in A', but for numbers below that, there may be no simple way to describe the set other than to list its elements.

By the way, the word "function" does not imply a "pattern" in any familiar sense; a function can look entirely random. What sort of function or pattern do you expect, and why?
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The main question is that:
1.Every partern's complement is pattern too... Because if you make up a pattern of universe by specific rule . So complement is pattern too...
For example Universe = Z+
My A cluster is 3x .
A' is 3x+1 and 3x+2 . So they are pattern too.

But does every function provide this ?
For that I make up a pattern. A={6xy+x-y,x,y € Z+ } And universe cluster is Z+

and I work to find a pattern for A'
If I find any pattern its okay.
 
I don't know what you mean by "pattern" and "pattern's complement". Are you using the word "pattern" to mean "set"? You also seem to be using "cluster" to mean "set". Language issues may be getting in our way here.

You appear to be using another example, saying that the set { 3x : x∈Z+ } has as its complement the set { 3x+1 : x∈Z+ } ∪ { 3x+2 : x∈Z+ }. Is that what you mean? (Actually, that isn't quite true, as the complement has to include 1 and 2.)

Not every set can be described in this way, if that is what you are asking.

In any case, I see no actual work to determine either A or A'. You don't seem to be making any progress.

Are you implying that this is not an exercise you were given (so that there is nothing to quote), but something you made up as an example? It would be very helpful if you would cooperate by telling us the context of the question.
 
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