Please give an example of a subset & a proper subset, explain the difference between a subset & proper subset.As we know, a set is just a...

Let us consider sets A and B. If every element of set A is
an element of set B, we say that A is a subset of B.

For
example if A is {1, 2, 3, 4, 5} and B is {1, 2, 3, 4, 5} then we can say A is a subset
of B as all the elements of set A are also elements of set B. Two sets which have the
same elements are subsets of each other. But A is not a proper subset of B in this
case.

For a set A to be a proper subset of another set B,
all the elements of A should be elements of B but A and B should not be equal. Or in
other words, A should be a subset of B but B should not be a subset of
A.

For example if A is {1, 2, 3, 4} and B is {1, 2, 3, 4,
5} then A is a proper subset of B. Here we see that all the elements of A are elements
of B but all elements of B are not elements of A. A is a subset of B but it is not equal
to B.