Question

Write down all the subsets of the following sets
(i) {a}

(ii) {a, b}

(iii) {1, 2, 3}

(iv) $\varphi$

Answer 1

We know that number of subsets of any set is $2^n$ where $n$ is the number of elements in that set.
Every non-empty set has two subsets $\varphi$ and the set itself.
(i) The subsets of $\left\{a\right\}$ are $\varphi$ and $\left\{a\right\}$.
(ii) The subsets of $\{a,b\}$ are $\varphi ,\left\{a\right\},\left\{b\right\},and\{a,b\}$.
(iii) The subsets of $\{1,2,3\}$ are $\varphi ,\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{2,3\},\{1,3\},and\{1,2,3\}$
(iv) The only subset of $\varphi$ is $\varphi$.