PixieDust1
  • PixieDust1
=
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
PixieDust1
  • PixieDust1
I got 0 idea how to solve this
myininaya
  • myininaya
You don't have to solve anything. It is is asking which of the below statements are true.
PixieDust1
  • PixieDust1
Or how to even see which statements are true. I got nothin'

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

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