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# Write down all the possible subsets of the following set$\left\{ {1,\left\{ 1 \right\}} \right\}$.  Answer Verified
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.
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