Assume that set A is a subset of set B. If sets A and B are equal (they contain the same elements), then A is NOT a proper subset of B, otherwise, it is.
Let A be the set {1,2,3,4} B is {1,2} and B is a proper subset of AC is {1} and C is also a proper subset of A.B and C are proper subsets of the set A because they are strictly contained in A....