Understanding Set Theory and Identifying Elements: W and X Sets Explained

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In summary, null set is an element of null set, and the 0 with the diagonal strike through it is the null set.
  • #1
mr_coffee
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Hello everyone! We just started set theroy and i just need to make sure I'm right about this...

THe question says:
Indicate the elements in each set dfined in a-f.

e. W = {t is in Z | -1 < t < -3 }
f. X = { u in Z | u <= 4 or u >= 1 }

for e. I said it would be No elemnts in the set, becuase there is no overlapping if you draw it on a number line nor is it possible to be greater than -1 and also be less than -3.'

for f.
i said {1,2,3,4}
but is this wrong because its an or problem, if its or, does that mean its all Z every integer is in the set? I think its Z everything intger is in the set now that i type this...

also for b.
T = { m is in Z | m = 1 + (-1)^i, for some integer i}
{ 0, 2}#2.
is O with a cross through it, the null set an element of {NULL SET}?
I said no becuase the null set has no elements, its an empty set. So an empty set cannot be in a set with only 1 element, {NULL SET}#3.
Is NULL set an element of Null set?
This one confused me...
its like saying is 2 in 2...
I said yes, because a an empty element is equal to an empty element like 2 is equal to 2...or am i misunderstanding this? I know if A is a subset of B and B is a sebset of A then A = B. But in this case its not saying they are subsets...they are uusing the "in" notation that looks like a small e.

thanks!
 
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  • #2
The top part looks good (you're right to question your original answer to f). For 2, what exactly is the set? Is it the set containing the single element the null set? If so the answer is obvious. Remember, the null set isn't "nothing", it's a set, just one that contains no elements. This should also help you answer 3.
 
  • #3
For 2, what exactly is the set? Is it the set containing the single element the null set?

I'm confused on the difference between NULL and {NULL}

I know the difference between 2 and {2}.
2 is the number itself, while {2} is a set that contains the number 2.
so {2} != 2.

The book does the following example
{Ann} denotes the set whose only element is Ann. whereas the word Ann denotes Ann herself. Since thsee are different {Ann} != Ann.
But if they said, Is Ann in {Ann} would this be true?
I think so... becuase they just said {Ann} is a set whose only element is Ann so Ann is in {Ann}.

Does just the NULL mean a set with no elements in it, and the {NULL} is a set with just 1 element, the NULL?

I looked in this chapter and it doesn't define what the 0 with the diagnoal strike through it means. I just remember seeing it in pervious math courses and I remember them calling it the NULL.

{2} is in {{1},{2}} this is true, becuase the set {2} is listed in the elements of {{1},{2}}.

So...
#2. is asking, is NULL in {NULL}
This would be false because NULL is not in {NULL}, because {NULL} is a set that only contains {NULL} while NULL is an empty set? But is NULL even a set? its like saying is 2 in {2} this is false, 2 is not in the set {2}, set {2} could have anything in it right? they never defined what {2} contains...It could be like {2} = {1,4,9,10} right?

The books example was: {2} in {1,2,3} which they said was false.#3. is NULL in NULL?
No, NULL contains nothing, so nothing cannot be in nothing I'm assuming.
-----------------------------------------------------------------------

Okay I've read it over again and this is my final answer hah...

c. Is Null in {Null}
Yes, Null is in the set {Null}. Because {Null} is the set that contains 1 element Null.

d. Is NULL in NULL.
No, Null contains no elements, so cannot be in Null.
 
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  • #4
By NULL you probably mean the empty set, sometimes also called the null set, and usually denoted by [itex]\emptyset[/itex]. This is the set containing no elements. But it is still a set. [itex]\emptyset[/itex] is not "nothing" any more than 0 is, and the set {[itex]\emptyset[/itex]} is just as valid a set as {0} or {23}, and they all contain a single element. [itex]\emptyset[/itex] contains 0 elements, {[itex]\emptyset[/itex]} contains 1 element.
 
  • #5
Thank u that makes much more sense!
and yes that is the LateX graphic i was trying to make!
 

What is an easy set question?

An easy set question is a type of question that is designed to be simple and straightforward, making it easier for the person answering to provide a correct response.

Why is it important to make sure a question is easy to answer?

It is important to make sure a question is easy to answer because it increases the chances of getting accurate and reliable responses. It also makes it easier for the person answering to provide a response, leading to a better overall experience for both the researcher and the participant.

How can I know if a question is easy to answer?

One way to determine if a question is easy to answer is to pilot test it with a small group of people and gather feedback on the difficulty level. Another way is to use clear and concise language and avoid complex sentence structures or unfamiliar terms.

What are some common mistakes to avoid when creating an easy set question?

Common mistakes to avoid when creating an easy set question include using double negatives, asking multiple questions in one, using vague or ambiguous language, and including too many options in a multiple-choice question.

Can an easy set question still be effective in gathering data?

Yes, an easy set question can still be effective in gathering data as long as it is designed to elicit the specific information needed and is clear and easy to understand for the participants. However, it is important to balance the simplicity of the question with its effectiveness in achieving the research goals.

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