We derive them by going back to the definitions of intersection , union , universal set and empty set , and by considering whether a given element is in, or not in, one or more sets. The laws listed below can be described as the Foundational Rules of Set Theory. Definition. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions. Note that in the second identity, we show the number of elements in each set by the corresponding shaded area. Set theory - Set theory - Operations on sets: The symbol ∪ is employed to denote the union of two sets. Set Theory: Solved Examples Q.6. Figure 1.16 pictorially verifies the given identities. 12 people chose Ice Tea & Ice cream, 8 people chose Ice Cream & Cold Coffee., 3 people chose Cold Coffee & Ice tea. Both laws and theories depend on basic elements of the scientific method, such as generating a hypothesis, testing that premise, finding (or not finding) empirical evidence and coming up with conclusions.Eventually, other scientists must be able to replicate the results if the experiment is destined to become the basis for a widely accepted law or theory. The notion of set is taken as “undefined”, “primitive”, or “basic”, so we don’t try to define what a set is, but we can give an informal description, describe important properties of sets, and give examples. A set is a collection of objects. We now consider the basic set identities that relate the various set operations. Thus, the set A ∪ B—read “A union B” or “the union of A and B”—is defined as the set that consists of all elements belonging to either set A or set B (or both). 1 person consumed all three. Distributive Law states that, the sum and product remain the same value even when the order of the elements is altered. Set theory has its own notations and symbols that can seem unusual for many. In a party of 120 people, 60 people will choose Ice tea, 24 people will choose Ice cream and 17 people will choose Cold Coffee. Distributive Law of Set Theory Proof - Definition. Solution. The sets \(A,\) \(B,\) \(C\) below are subsets of a universal set \(U.\) Identity Laws In this tutorial, we look at some solved examples to understand how set theory works and the kind of problems it can be used to solve. It is usually represented in flower braces.