For each of the ff. sets, determine whether 2 is an element of that set.
a. {๐ฅโโ|๐ฅ ๐๐ ๐๐ ๐๐๐ก๐๐๐๐ ๐๐๐๐๐ก๐๐ ๐กโ๐๐ 1}
b. {๐ฅโโ|๐ฅ ๐๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐๐ ๐๐ ๐๐๐ก๐๐๐๐}
c. {2,{2}}
d. {{2},{{2}}}
Solution (a)
The given set is { ๐๐ ๐๐ ๐๐๐ก๐๐๐๐ ๐๐๐๐๐ก๐๐ ๐กโ๐๐ 1} can be written as
It is clear that 2 \in \{ ๐๐ ๐๐ ๐๐๐ก๐๐๐๐ ๐๐๐๐๐ก๐๐ ๐กโ๐๐ 1}
Hence 2 is an element of that set.
Solution (b)
The given set is { ๐๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐๐ ๐๐ ๐๐๐ก๐๐๐๐} can be written as
\left\{ {{1^2},\,{2^2},\,{3^2},\,....} \right\}\
\left\{ {1,\,\,4,\,\,9,\,\,....} \right\}\
We can see that 2 \in \left\{ {1,\,\,4,\,\,9,\,\,....} \right\}\
Hence 2 \notin \ {๐ฅโโ|๐ฅ ๐๐ ๐กโ๐ ๐ ๐๐ข๐๐๐ ๐๐ ๐๐ ๐๐๐ก๐๐๐๐}
Hence 2 is not an element of that set
Solution (c)
The given set is {2,{2}} can be written as
We can see that
Hence 2 is an element of that set
Solution (d)
The given set is can be written as
We can see that
Hence 2 is not an element of that set
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