Can any set be a proper subset of itself & please give an example of why or why not?As we know, a set is just a collection of objects that are...

First, let's consider the definition of a subset
and a proper subset: We say that a set A is a
subset of a set B if every element in A also exists in B. We say
that A is a proper subset of B if A is a subset of B and there
exists at least one element in B that does not exist in
A.

A set cannot be a proper subset of
itself.

Proof:

Let A be a set.
Suppose, for contradiction, that A is a proper subset of itself. By definition of proper
subset, then there exists some element in A that does not exist in A.
Therefore a set cannot be a proper subset of
itself.