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• give examples and non-examples of sets, relations and functions • perform different operations on sets • establish relationships between operations on sets and those on statements in logic • use Venn diagrams • explain the difference between a relation and a function. • describe different types of relations and functions.
This chapter will be devoted to understanding set theory, relations, functions. We start with the basic set theory. 1.1 Sets Mathematicians over the last two centuries have been used to the idea of considering a collection of objects/numbers as a single entity. These entities are what are typically called sets. The technique of
Basic Concepts of Set Theory. 1.1. Sets and elements. Set theory is a basis of modern mathematics, and notions of set theory are used in all formal descriptions.
parallel to line m, set A is a subset of set B. In all these, we notice that a relation involves pairs of objects in certain order. In this Chapter, we will learn how to link pairs of objects from two sets and then introduce relations between the two objects in the pair. Finally, we will learn about special relations which will qualify to be ...
Definition 1 A relation R in a set A is called empty relation, if no element of A is related to any element of A, i.e., R = φ ⊂ A × A. Definition 2 A relation R in a set A is called universal relation, if each element of A is related to every element of A, i.e., R = A × A.
Michael Franke. Basic notions of (naïve) set theory; sets, elements, relations between and operations on sets; relations and their properties; functions and their properties. Examples of informal proofs: direct, indirect and counterexamples.
