## PixieDust1 2 years ago =

1. PixieDust1

I got 0 idea how to solve this

2. myininaya

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

3. PixieDust1

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

4. 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.

5. myininaya

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

6. myininaya

Does Z have all the elements that W has?

7. PixieDust1

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

8. 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.

9. myininaya

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

10. PixieDust1

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

Yes

12. myininaya

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

13. myininaya

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

14. myininaya

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

15. PixieDust1

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

16. PixieDust1

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

17. 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.

18. myininaya

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

19. PixieDust1

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

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

21. myininaya

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

22. PixieDust1

Yuppers!

23. myininaya

24. PixieDust1

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

25. PixieDust1

In both directions :D

26. myininaya

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

27. PixieDust1

I think so!

28. myininaya

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

29. PixieDust1

Hmmm... maybe it means like no value?

30. PixieDust1

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

31. myininaya

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

32. 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.

33. PixieDust1

But its apart of every set, right?

34. myininaya

It is a subset of every set.

35. PixieDust1

okay! So then would that make them true?

36. myininaya

Yep

37. PixieDust1

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

38. myininaya

equal

39. PixieDust1

|dw:1387243554944:dw|

40. myininaya

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

41. myininaya

Is that true? Are these the same sets?

42. PixieDust1

I don't think so

43. PixieDust1

Oh wait!!! I think they may be!

44. myininaya

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

45. PixieDust1

there wouldn't be any

46. myininaya

what?

47. myininaya

The whole numbers are defined for you in your problem

48. PixieDust1

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

49. myininaya

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

50. PixieDust1

Oh yeah!

51. 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)

52. PixieDust1

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

53. myininaya

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

54. myininaya

The last one, can you tell me the answer?

55. PixieDust1

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

56. 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.

57. PixieDust1

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

58. myininaya

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

59. myininaya

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

60. PixieDust1

Oh wow

61. PixieDust1

Thank you SOOOOO much for helping me out!

62. PixieDust1

I really understand this now

63. PixieDust1

:D

64. myininaya

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

65. PixieDust1

Thanks! Have an awesome day :D