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mathmath333

  • one year ago

Set Theory

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  1. mathmath333
    • one year ago
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    |dw:1438630180668:dw|

  2. mathmath333
    • one year ago
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    I think 2,4,7 and 9 are correct

  3. freckles
    • one year ago
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    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.

  4. freckles
    • one year ago
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    why do you think iii is wrong?

  5. freckles
    • one year ago
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    {{3,4}} is the set containing the element {3,4} isn't it? isn't the element {3,4} also in A?

  6. mathmath333
    • one year ago
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    oh 3 is also correcr sry

  7. mathmath333
    • one year ago
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    yep

  8. freckles
    • one year ago
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    and what about vi?

  9. freckles
    • one year ago
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    I think you got vi and vii mixed up

  10. mathmath333
    • one year ago
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    vi is correct ?

  11. freckles
    • one year ago
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    and also you mixed up xi and x

  12. mathmath333
    • one year ago
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    i think (vi) is incorrect

  13. ganeshie8
    • one year ago
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    |dw:1438630730330:dw|

  14. mathmath333
    • one year ago
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    is red one's correct or incorrect

  15. freckles
    • one year ago
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    red is incorrect

  16. ganeshie8
    • one year ago
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    |dw:1438630888592:dw|

  17. mathmath333
    • one year ago
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    lol i am confused with difference between \(\color{red}{a}\) and \(\color{red}{\{a\}}\)

  18. freckles
    • one year ago
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    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

  19. mathmath333
    • one year ago
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    no, i mean what is the difference between the not for particularly empty set example \(\color{red}{\{1\}}\) and \(\color{red}{1}\)

  20. ganeshie8
    • one year ago
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    \(a\) : This is an \(element\), \(a\) \(\{a\}\) : This is a \(set\) which contains a single element, \(a\)

  21. freckles
    • one year ago
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    \[B=\left\{ \emptyset,a \right\} \text{ here we have } \emptyset \in B \text{ but we also have } \emptyset \subseteq B\]

  22. mathmath333
    • one year ago
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    ok i see that is a set

  23. freckles
    • one year ago
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    we said emptyset was a member of that set because it is actually in that set

  24. ganeshie8
    • one year ago
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    as you can see, sets can contain other sets as elements in them.

  25. mathmath333
    • one year ago
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    ii am confused about the last one also \(\{\emptyset\}\subset A\) this is true ?

  26. mathmath333
    • one year ago
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    as empty set is a subset of every set

  27. mathmath333
    • one year ago
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    i think the last one is true

  28. freckles
    • one year ago
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    \[B=\left\{ \emptyset,a \right\} \text{ here we have } \emptyset \in B \text{ but we also have } \emptyset \subseteq B \\ \text{ also } a \in B \text{ but } a \cancel{ \subseteq} B \text{ but } \{a\} \subseteq B \\ \] 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?

  29. mathmath333
    • one year ago
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    frekels i don't understand how is this true in ur above sentense \(\emptyset \subseteq B\)

  30. freckles
    • one year ago
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    the empty set is a set and the empty set is a subset of any set

  31. mathmath333
    • one year ago
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    but that sign is of proper set right \(\Huge \subseteq\)

  32. freckles
    • one year ago
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    oh I never used that as the meaning for that notation

  33. freckles
    • one year ago
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    https://en.wikipedia.org/wiki/Subset as you see here people have different meanings for the notations

  34. freckles
    • one year ago
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    I always used that one thing to mean subset of

  35. ganeshie8
    • one year ago
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    \[\emptyset = \{~~\}\]

  36. freckles
    • one year ago
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    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

  37. mathmath333
    • one year ago
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    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 \(B=\left\{ \emptyset,a \right\}\)

  38. freckles
    • one year ago
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    what

  39. freckles
    • one year ago
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    \[B =\{ \emptyset, a\} \text{ I never said } B =\{ \emptyset\} \text{ \in my example }\]

  40. freckles
    • one year ago
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    \[\emptyset \subseteq X \text{ is always true for any set} X\] 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

  41. freckles
    • one year ago
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    this is what I mean by empty set is a subset of every set

  42. zzr0ck3r
    • one year ago
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    often \(\subset\) and \(\subseteq\) are used interchangeably

  43. ParthKohli
    • one year ago
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    NCERT hehe

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