### Theory:

A subset of a set is said to be proper if all the elements of the subset are in the set but at least one element of the set which is not present in the subset. If a subset $$A$$ is a proper subset of $$B$$, then there exist at least one element of set $$B$$ is not in subset $$A$$. It is denoted as $A\subset B$.
Important!
A proper subset of a set is a subset that is not exactly equal to the set itself.
Example:
Consider the set $$A=\{$$Saffron, White, Green$$\}$$ and $$B=\{x:x$$ is a colour in national flag$$\}$$.

Here the set $$A$$ is direct. Set $$B$$ takes the colours in the national flag.

Our Indian national flag is made up of four colours. They are Saffron, White, Blue and Green.

The set $$B=\{$$Saffron, White, Blue, Green$$\}$$.

Here all the element in set $$A$$ is present in set $$B$$ as well. So $$A$$ is a subset of $$B$$.

Let us observe the set $$B$$.

Here comes an element Blue $$\in B$$ is not present in the subset $$A$$. Thus, by the definition of proper subset, the set $$B$$ is a proper subset of $$A$$.