Set Theory

- mathmath333

Set Theory

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- mathmath333

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- mathmath333

http://assets.openstudy.com/updates/attachments/55bfab49e4b033255003597a-mathmath333-1438630105708-c88889apture.png

- mathmath333

I think 2,4,7 and 9 are correct

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## More answers

- 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

why do you think iii is wrong?

- freckles

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

- mathmath333

oh 3 is also correcr sry

- mathmath333

yep

- freckles

and what about vi?

- freckles

I think you got vi and vii mixed up

- mathmath333

vi is correct ?

- freckles

and also you mixed up xi and x

- mathmath333

i think (vi) is incorrect

- ganeshie8

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- mathmath333

is red one's correct or incorrect

- freckles

red is incorrect

- ganeshie8

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- mathmath333

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

- 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

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

- ganeshie8

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

- freckles

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

- mathmath333

ok i see that is a set

- freckles

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

- ganeshie8

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

- mathmath333

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

- mathmath333

as empty set is a subset of every set

- mathmath333

i think the last one is true

- 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

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

- freckles

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

- mathmath333

but that sign is of proper set right \(\Huge \subseteq\)

- freckles

oh I never used that as the meaning for that notation

- freckles

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

- freckles

I always used that one thing to mean subset of

- ganeshie8

\[\emptyset = \{~~\}\]

- 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

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

what

- freckles

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

- 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

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

- zzr0ck3r

often \(\subset\) and \(\subseteq\) are used interchangeably

- ParthKohli

NCERT hehe

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