Sets

After completion of this chapter, students will be able to:

  • find the cardinality of A ∪ B, A ∩ B, A - B, (A ∪ B)c,  \(\overline A\) ∩ B, A ∩ \(\overline B\), (A ∩ B)c etc.
  • solve the word problems of two sets using Venn- diagram.
  • get acquainted with word problems involving three sets using venn- diagram.

Notes

Introduction to Sets

In the early twentieth century, John-Euler Venn solved the word problems in arithmetic with the help of Venn-diagram. This method grew popular as it is easy to understand and simple to calculate. So, Venn-diagram is associated with his name. There are 6 types of sets, they are as follow: Empty set, Singleton set, Finite set, Infinite set, Equivalent set & Equal set.

Cardinality of a set

The number of distinct element in a given set A is called the cardinal number of A. It is denoted by n(A). If A = { 1, 2, 3, 4, 5 }, then the cardinality of set A is denoted by n (A) = 5.