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

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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, because 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 because 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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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.
 
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... because 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, because 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.
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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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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.
 
Thank u that makes much more sense!
and yes that is the LateX graphic i was trying to make!