Algebra: Abstract and Modern

1

Sets and Relations

1.1 Sets and Subsets

1.2 Relations and Functions

1.3 Equivalence Relations and Partitions

1.4 The Cardinality of a Set

The concept of a set was used even by the ancient mankind without having an exact idea of what it was. In modern mathematics, the notion of a set is most basic. In fact, almost all the mathematical systems are certain collection of sets and their theories can be categorised as parts of set theory. We do not intend to discuss axiomatic development of set theory. But, any person with an intention of starting to learn the present day algebra must necessarily possess certain elementary knowledge of set theory. This chapter provides a fairly good platform to refresh with those elementary notions of sets, relations, ...