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Write down all the possible subsets of the following set
\[\left\{ {1,\left\{ 1 \right\}} \right\}\].

Last updated date: 17th Jul 2024
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Hint: if a set has m elements then it has \[{2^m}\] subsets. E.g. if a set has 1 element then it has \[{2^1}\]subsets, namely itself and the null set\[\left( \phi \right)\]. Therefore we start with counting the no. of elements.

Here in the set \[\left\{ {1,\left\{ 1 \right\}} \right\}\], we have 2 elements and that are 1 and\[\left\{ 1 \right\}\]
∴ It have \[{2^2}\] subsets i.e. 4 subsets
∴ The above set have \[\phi ,1\] \[\left\{ 1 \right\}\]and\[\left\{ {1,\left\{ 1 \right\}} \right\}\] subsets.

Note: 1. A set is a well-defined collection of objects.
           2. An object in a set is called an element of the set.
           3. A set that contains no elements is called a null set or empty set.