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## PixieDust1 Group Title Select all of the following true statements if R = real numbers, Z = integers, and W = {0, 1, 2, ...}. Wc Z R cW 0e Z Øc R {0, 1, 2, ...}c W - c had line underneath is -2 eW 7 months ago 7 months ago

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1. PixieDust1 Group Title

I got 0 idea how to solve this

2. myininaya Group Title

You don't have to solve anything. It is is asking which of the below statements are true.

3. PixieDust1 Group Title

Or how to even see which statements are true. I got nothin'

4. myininaya Group Title

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.

5. myininaya Group Title

So let's look at the first statement "W is a subset of Z" Do you think that is true?

6. myininaya Group Title

Does Z have all the elements that W has?

7. PixieDust1 Group Title

It looks true to me!! All w are z, but not all z are w

8. myininaya Group Title

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.

9. myininaya Group Title

Do you think the real numbers are a subset of the whole numbers?

10. PixieDust1 Group Title

That makes sense!! Thanks! :D Based on that, I think #2 is true All r is w, but all w is not r

11. PixieDust1 Group Title

Yes

12. myininaya Group Title

Well the real numbers are definitely not a subset of the whole numbers.

13. myininaya Group Title

The real numbers include numbers that aren't in the set of whole numbers like sqrt(5) and pi and so on...

14. myininaya Group Title

Now you could say the whole numbers is a subset of the real numbers.

15. PixieDust1 Group Title

Oh i forgot! Silly me! I get confused very quickly. That makes sense to me!

16. PixieDust1 Group Title

What does the "e" mean on the next one?

17. myininaya Group Title

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.

18. myininaya Group Title

|dw:1387243116999:dw| The symbol should look more like this.

19. PixieDust1 Group Title

Yeah, I used the standard keyboard symbol for the regular e. The e you drew is what it was suppose to look like :)

20. myininaya Group Title

So that statement is asking you if you think that element 0 is in the set of integers

21. myininaya Group Title

The integers are {...,-3,-2,-1,0,1,2,3...} Do you think 0 is in that set?

22. PixieDust1 Group Title

Yuppers!

23. myininaya Group Title

what about 5000?

24. PixieDust1 Group Title

Yup! Forever and ever and ever and ever and ever ....

25. PixieDust1 Group Title

In both directions :D

26. myininaya Group Title

Those dots mean it continues on in both directions.. Good stuff. Okay so that one you say is true.

27. PixieDust1 Group Title

I think so!

28. myininaya Group Title

So do you know what that other symbol means in the next statement?

29. PixieDust1 Group Title

Hmmm... maybe it means like no value?

30. PixieDust1 Group Title

I saw it in the textbook, but they never told us what it meant They just started using it

31. myininaya Group Title

$\emptyset=\{ \text{ } \}=\text{ empty set }$ This basically means there are no elements contained within the set.

32. myininaya Group Title

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.

33. PixieDust1 Group Title

But its apart of every set, right?

34. myininaya Group Title

It is a subset of every set.

35. PixieDust1 Group Title

okay! So then would that make them true?

36. myininaya Group Title

Yep

37. PixieDust1 Group Title

Cool! I didn't understand what the line under the c on the next one is

38. myininaya Group Title

equal

39. PixieDust1 Group Title

|dw:1387243554944:dw|

40. myininaya Group Title

Like I'm saying that equal sign means they could be equal. Like they have the same exact elements in both sets.

41. myininaya Group Title

Is that true? Are these the same sets?

42. PixieDust1 Group Title

I don't think so

43. PixieDust1 Group Title

Oh wait!!! I think they may be!

44. myininaya Group Title

So what is the whole numbers then if it isn't {0,1,2,...}

45. PixieDust1 Group Title

there wouldn't be any

46. myininaya Group Title

what?

47. myininaya Group Title

The whole numbers are defined for you in your problem

48. PixieDust1 Group Title

Isn't 0,1,2 etc whole numbers?

49. myininaya Group Title

Yes so back to your question, |dw:1387243864499:dw| are these the same sets on both sides of that "weird symbol"?

50. PixieDust1 Group Title

Oh yeah!

51. myininaya Group Title

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)

52. PixieDust1 Group Title

oh! So it's kinda like an equal sign (in a way)? If so, I think this is true

53. myininaya Group Title

Yep It means it can be a subset of that set or subset of that set that is that set (or equal)

54. myininaya Group Title

The last one, can you tell me the answer?

55. PixieDust1 Group Title

For the last one, i think it is false. -2 is not equal to W (a whole number)

56. myininaya Group Title

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.

57. PixieDust1 Group Title

Oh yeah! Because its the element that includes the entire w

58. myininaya Group Title

People sometimes use this notation to say it is not an element of : |dw:1387244283183:dw|

59. myininaya Group Title

They just put a mark through the sign that means an element of to say that it is not an element of

60. PixieDust1 Group Title

Oh wow

61. PixieDust1 Group Title

Thank you SOOOOO much for helping me out!

62. PixieDust1 Group Title

I really understand this now

63. PixieDust1 Group Title

:D

64. myininaya Group Title

No problem. Cool stuff. I'm glad you do. May the force be with you in your future math studies!

65. PixieDust1 Group Title

Thanks! Have an awesome day :D