Sets and Propositions

This chapter is devoted to an elementary introduction to sets theory and propositions. We define some fundamental concepts of sets and introduce several types of sets. We study the algebra of sets and define the cardinal number, which is the number of elements of a finite set and its applications. We presented some results related to the cardinality of a finite set by the principle of inclusion and exclusion. We will also consider a related subject to the theory of sets, namely the theory of propositions. After an introduction to propositions and predicate logic, we discuss operations on propositions by using truth tables and their applications on mathematical problems through different mathematical proofs.