Some Set Theory Rules

In mathematics, we follow some rules for the representation of sets. The rules are;

• The name of the set is denoted by uppercase letters
•  The elements, members or objects of the sets are denoted by lowercase letters

Universal Set

The set under consideration is likely to be the subsets of a fixed or a global set. This fixed or global set is called the Universal Set. A universal set is the set of all objects of interest in a particular discussion. This set can be very big or small depending on the context

For example, if we are discussing medical students at Nnamdi Azikwe University, the whole students of the Nnamdi Azikwe University can be our universal set. If our reference is to persons, every person in the Nnamdi Azikwe University can be the universal set. Therefore, the universal set varies as our group of references varies. The universal set is usually denoted by U

Equal Set

Two sets are equal If they have precisely the same members. Now, at first glance they may not seem equal, we may have to examine them closely

Example: Are A and B equal? Where
A is the set whose members are the first four positive whole numbers

B= {4, 2, 1, 3 }

Let’s check. They both contain 1,2,3,4 So they are equal.

The equals sign (=) is used to show equality.

Therefore, A= B

Empty or Null Set

There are no elements in this set. It is represented by { } or Ø