Consider the given set.
\(\left\{ {x \in \left. {\rm{R}} \right|x\;{\rm{is an integer greater than 1}}} \right\}\)
The given set contain \(2\) but it does not contain set \(\left\{ 2 \right\}\). Therefore, \(\left\{ 2 \right\}\) is not an element of the given set.
Consider the given set.
\(\left\{ {x \in \left. {\rm{R}} \right|x\;{\rm{is the}}\;{\rm{square}}\;{\rm{of}}\;{\rm{an}}\;{\rm{integer}}} \right\}\)
The given set contains all squares of integers, and \(\left\{ 2 \right\}\) is not the square of any integer.
Therefore, \(\left\{ 2 \right\}\) is not an element of the given set.
Consider the given set.
\(\left\{ {2,\;\left\{ 2 \right\}} \right\}\)
The given set contains a subset \(\left\{ 2 \right\}\).
Therefore, \(\left\{ 2 \right\}\) is an element of the given set.
Consider the given set.
\(\left\{ {\left\{ 2 \right\},\;\left\{ {\left\{ 2 \right\}} \right\}} \right\}\)
The set contains the subset \(\left\{ 2 \right\}\) on left.
Therefore, \(\left\{ 2 \right\}\) is an element of the given set.
Consider the given set.
\(\left\{ {\left\{ 2 \right\},\;\left\{ {2,\;\left\{ 2 \right\}} \right\}} \right\}\)
The set contains the subset \(\left\{ 2 \right\}\).
Therefore, \(\left\{ 2 \right\}\) is an element of the given set.
Consider the given set.
\(\left\{ {\left\{ {\left\{ 2 \right\}} \right\}} \right\}\)
The set contains the subset \(\left\{ {\left\{ 2 \right\}} \right\}\) not \(\left\{ 2 \right\}\).
Therefore, \(\left\{ 2 \right\}\) is not an element of the given set.
