Question

Write down all possible proper subsets each of the following sets:
(i) $\{1,2\}$
(ii) $\{1,2,3\}$
(iii) $\left\{1\right\}$.

Answer 1

If set $A$ is sub set of set $B$ then all the elements of set $A$ must be present in set $B$.
If a subset $X$ is not equal to set $B$ then set $X$ is a proper subset of $B$.
Null set $\left(\varphi \right)$ be always proper subset of any set.

(i) Given set $\{1,2\}$
The possible proper subsets are $\varphi ,\left\{1\right\},\left\{2\right\}$
(ii) Given set $\{1,2,3\}$
The possible proper subsets are $\varphi ,\left\{1\right\},\left\{2\right\},\left\{3\right\},\{1,2\},\{1,3\},\{2,3\}$
(iii) Given set $\left\{1\right\}$
The only possible proper subset is $\varphi ,\left\{1\right\}$