mathmath333
  • mathmath333
Set Theory
Mathematics
schrodinger
  • schrodinger
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mathmath333
  • mathmath333
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mathmath333
  • mathmath333
http://assets.openstudy.com/updates/attachments/55bfab49e4b033255003597a-mathmath333-1438630105708-c88889apture.png
mathmath333
  • mathmath333
I think 2,4,7 and 9 are correct

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freckles
  • 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.
freckles
  • freckles
why do you think iii is wrong?
freckles
  • freckles
{{3,4}} is the set containing the element {3,4} isn't it? isn't the element {3,4} also in A?
mathmath333
  • mathmath333
oh 3 is also correcr sry
mathmath333
  • mathmath333
yep
freckles
  • freckles
and what about vi?
freckles
  • freckles
I think you got vi and vii mixed up
mathmath333
  • mathmath333
vi is correct ?
freckles
  • freckles
and also you mixed up xi and x
mathmath333
  • mathmath333
i think (vi) is incorrect
ganeshie8
  • ganeshie8
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mathmath333
  • mathmath333
is red one's correct or incorrect
freckles
  • freckles
red is incorrect
ganeshie8
  • ganeshie8
|dw:1438630888592:dw|
mathmath333
  • mathmath333
lol i am confused with difference between \(\color{red}{a}\) and \(\color{red}{\{a\}}\)
freckles
  • 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
mathmath333
  • mathmath333
no, i mean what is the difference between the not for particularly empty set example \(\color{red}{\{1\}}\) and \(\color{red}{1}\)
ganeshie8
  • ganeshie8
\(a\) : This is an \(element\), \(a\) \(\{a\}\) : This is a \(set\) which contains a single element, \(a\)
freckles
  • freckles
\[B=\left\{ \emptyset,a \right\} \text{ here we have } \emptyset \in B \text{ but we also have } \emptyset \subseteq B\]
mathmath333
  • mathmath333
ok i see that is a set
freckles
  • freckles
we said emptyset was a member of that set because it is actually in that set
ganeshie8
  • ganeshie8
as you can see, sets can contain other sets as elements in them.
mathmath333
  • mathmath333
ii am confused about the last one also \(\{\emptyset\}\subset A\) this is true ?
mathmath333
  • mathmath333
as empty set is a subset of every set
mathmath333
  • mathmath333
i think the last one is true
freckles
  • 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?
mathmath333
  • mathmath333
frekels i don't understand how is this true in ur above sentense \(\emptyset \subseteq B\)
freckles
  • freckles
the empty set is a set and the empty set is a subset of any set
mathmath333
  • mathmath333
but that sign is of proper set right \(\Huge \subseteq\)
freckles
  • freckles
oh I never used that as the meaning for that notation
freckles
  • freckles
https://en.wikipedia.org/wiki/Subset as you see here people have different meanings for the notations
freckles
  • freckles
I always used that one thing to mean subset of
ganeshie8
  • ganeshie8
\[\emptyset = \{~~\}\]
freckles
  • 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
mathmath333
  • 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 \(B=\left\{ \emptyset,a \right\}\)
freckles
  • freckles
what
freckles
  • freckles
\[B =\{ \emptyset, a\} \text{ I never said } B =\{ \emptyset\} \text{ \in my example }\]
freckles
  • 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
freckles
  • freckles
this is what I mean by empty set is a subset of every set
zzr0ck3r
  • zzr0ck3r
often \(\subset\) and \(\subseteq\) are used interchangeably
ParthKohli
  • ParthKohli
NCERT hehe

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