## mathmath333 one year ago Set Theory

1. mathmath333

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2. mathmath333
3. mathmath333

I think 2,4,7 and 9 are correct

4. freckles

well i is incorrect since {3,4} is actually an element of A so it would have been correct if it said: $\{3,4\} \in A$ so you were right about ii.

5. freckles

why do you think iii is wrong?

6. freckles

{{3,4}} is the set containing the element {3,4} isn't it? isn't the element {3,4} also in A?

7. mathmath333

oh 3 is also correcr sry

8. mathmath333

yep

9. freckles

10. freckles

I think you got vi and vii mixed up

11. mathmath333

vi is correct ?

12. freckles

and also you mixed up xi and x

13. mathmath333

i think (vi) is incorrect

14. ganeshie8

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15. mathmath333

is red one's correct or incorrect

16. freckles

red is incorrect

17. ganeshie8

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18. mathmath333

lol i am confused with difference between $$\color{red}{a}$$ and $$\color{red}{\{a\}}$$

19. freckles

empty set is a set the empty set is a subset of any set the empty set is not always an element of a set

20. mathmath333

no, i mean what is the difference between the not for particularly empty set example $$\color{red}{\{1\}}$$ and $$\color{red}{1}$$

21. ganeshie8

$$a$$ : This is an $$element$$, $$a$$ $$\{a\}$$ : This is a $$set$$ which contains a single element, $$a$$

22. freckles

$B=\left\{ \emptyset,a \right\} \text{ here we have } \emptyset \in B \text{ but we also have } \emptyset \subseteq B$

23. mathmath333

ok i see that is a set

24. freckles

we said emptyset was a member of that set because it is actually in that set

25. ganeshie8

as you can see, sets can contain other sets as elements in them.

26. mathmath333

ii am confused about the last one also $$\{\emptyset\}\subset A$$ this is true ?

27. mathmath333

as empty set is a subset of every set

28. mathmath333

i think the last one is true

29. freckles

$B=\left\{ \emptyset,a \right\} \text{ here we have } \emptyset \in B \text{ but we also have } \emptyset \subseteq B \\ \text{ also } a \in B \text{ but } a \cancel{ \subseteq} B \text{ but } \{a\} \subseteq B \\$ answer to latest question but that is the set containing the empty set treat that empty set as an element is the empty set an element of A?

30. mathmath333

frekels i don't understand how is this true in ur above sentense $$\emptyset \subseteq B$$

31. freckles

the empty set is a set and the empty set is a subset of any set

32. mathmath333

but that sign is of proper set right $$\Huge \subseteq$$

33. freckles

oh I never used that as the meaning for that notation

34. freckles

https://en.wikipedia.org/wiki/Subset as you see here people have different meanings for the notations

35. freckles

I always used that one thing to mean subset of

36. ganeshie8

$\emptyset = \{~~\}$

37. freckles

the empty set is also a proper subset of every set exluding the empty set that is the empty set is not a proper subset of itself

38. mathmath333

i mean that first u specified that $$B=\left\{ \emptyset,a \right\}$$ and then u said that $$\emptyset \subseteq B$$ is true but for that B should be $$B=\{\emptyset \}$$ not $$B=\left\{ \emptyset,a \right\}$$

39. freckles

what

40. freckles

$B =\{ \emptyset, a\} \text{ I never said } B =\{ \emptyset\} \text{ \in my example }$

41. freckles

$\emptyset \subseteq X \text{ is always true for any set} X$ unless that one symbols means proper set and that case the only exception is X being the empty set this is what I mean by empty set if a subset of every set

42. freckles

this is what I mean by empty set is a subset of every set

43. zzr0ck3r

often $$\subset$$ and $$\subseteq$$ are used interchangeably

44. ParthKohli

NCERT hehe