Question

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

Answer 1

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.