Continiung from the title, it does not necessarilly follow that A will be a subset of C. I knew this for a long time, but I am unable to understand why. Elias zakons notes gave an example' here is the example: This may be illustrated by the following examples. Let a “nation” be defined as a certain set of individuals, and let the United Nations (U.N.) be regarded as a certain set of nations. Then single persons are elements of the nations, and the nations are members of U.N., but individuals are not members of U.N. Similarly, the Big Ten consists of ten universities, each university contains thousands of students, but no student is one of the Big Ten. Families of sets will usually be denoted by script letters: M, N , P, etc could anyone give other examples, more mathematical object oriented?