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 PixieDust1
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 Stacey Warren  Expert brainly.com
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 PixieDust1
I got 0 idea how to solve this
 myininaya
You don't have to solve anything. It is is asking which of the below statements are true.
 PixieDust1
Or how to even see which statements are true.
I got nothin'
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More answers
 myininaya
Every set is a subset of itself.

Empty set is a subset of every set.

Other
Example:
If A={1,2,3} and B={1,2}
B is a subset of A because A has all of B's elements.
A is not a subset of B because B does not have all the elements A has.
 myininaya
So let's look at the first statement "W is a subset of Z"
Do you think that is true?
 myininaya
Does Z have all the elements that W has?
 PixieDust1
It looks true to me!! All w are z, but not all z are w
 myininaya
Yep that statement is true.
Integers={...,3,2,1,0,1,2,3,...}
W={0,1,2,...}
As we see the set of W is a subset of Z because W has the elements 0,1,2,... and these elements are also in Z.
Now Z is not a subset of W because W does not have all the elements Z has.
 myininaya
Do you think the real numbers are a subset of the whole numbers?
 PixieDust1
That makes sense!! Thanks! :D
Based on that, I think #2 is true
All r is w, but all w is not r
 PixieDust1
Yes
 myininaya
Well the real numbers are definitely not a subset of the whole numbers.
 myininaya
The real numbers include numbers that aren't in the set of whole numbers like sqrt(5) and pi and so on...
 myininaya
Now you could say the whole numbers is a subset of the real numbers.
 PixieDust1
Oh i forgot! Silly me! I get confused very quickly.
That makes sense to me!
 PixieDust1
What does the "e" mean on the next one?
 myininaya
I think your e there is suppose to mean an element of, but that isn;'t the traditional symbol for it that you are using.
 myininaya
dw:1387243116999:dw
The symbol should look more like this.
 PixieDust1
Yeah, I used the standard keyboard symbol for the regular e. The e you drew is what it was suppose to look like :)
 myininaya
So that statement is asking you if you think that element 0 is in the set of integers
 myininaya
The integers are {...,3,2,1,0,1,2,3...}
Do you think 0 is in that set?
 PixieDust1
Yuppers!
 myininaya
what about 5000?
 PixieDust1
Yup! Forever and ever and ever and ever and ever ....
 PixieDust1
In both directions :D
 myininaya
Those dots mean it continues on in both directions.. Good stuff. Okay so that one you say is true.
 PixieDust1
I think so!
 myininaya
So do you know what that other symbol means in the next statement?
 PixieDust1
Hmmm... maybe it means like no value?
 PixieDust1
I saw it in the textbook, but they never told us what it meant They just started using it
 myininaya
\[\emptyset=\{ \text{ } \}=\text{ empty set } \]
This basically means there are no elements contained within the set.
 myininaya
It is totally empty and no you do not say 0 is element of the empty set. There are no elements in the empty set not even 0.
 PixieDust1
But its apart of every set, right?
 myininaya
It is a subset of every set.
 PixieDust1
okay! So then would that make them true?
 myininaya
Yep
 PixieDust1
Cool! I didn't understand what the line under the c on the next one is
 myininaya
equal
 PixieDust1
dw:1387243554944:dw
 myininaya
Like I'm saying that equal sign means they could be equal. Like they have the same exact elements in both sets.
 myininaya
Is that true?
Are these the same sets?
 PixieDust1
I don't think so
 PixieDust1
Oh wait!!! I think they may be!
 myininaya
So what is the whole numbers then if it isn't {0,1,2,...}
 PixieDust1
there wouldn't be any
 myininaya
what?
 myininaya
The whole numbers are defined for you in your problem
 PixieDust1
Isn't 0,1,2 etc whole numbers?
 myininaya
Yes so back to your question, dw:1387243864499:dw
are these the same sets on both sides of that "weird symbol"?
 PixieDust1
Oh yeah!
 myininaya
that little line just means they can have all the exact same elements (talking about both sets; both sets can be exactly the same when you have symbol)
 PixieDust1
oh! So it's kinda like an equal sign (in a way)?
If so, I think this is true
 myininaya
Yep
It means it can be a subset of that set or subset of that set that is that set (or equal)
 myininaya
The last one, can you tell me the answer?
 PixieDust1
For the last one, i think it is false. 2 is not equal to W (a whole number)
 myininaya
You are right to say false. But doesn't say "2 is not equal to W"
Say "2 is not en element of W"
This just means the set W does not include 2 as an element.
 PixieDust1
Oh yeah! Because its the element that includes the entire w
 myininaya
People sometimes use this notation to say it is not an element of :
dw:1387244283183:dw
 myininaya
They just put a mark through the sign that means an element of to say that it is not an element of
 PixieDust1
Oh wow
 PixieDust1
Thank you SOOOOO much for helping me out!
 PixieDust1
I really understand this now
 PixieDust1
:D
 myininaya
No problem. Cool stuff. I'm glad you do. May the force be with you in your future math studies!
 PixieDust1
Thanks! Have an awesome day :D
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