Representation of a Set

There are three standard ways to describe or represent a set:

1. ROSTER or Tabular or List method: every element of the set is written out explicitly inside braces $\{,\}$, separated by commas. For example, if B is the set of all days in a week, then $B = \{\text{Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday}\}$; if C is the set of all vowels in the English alphabet, then $C=\{a,e,i,o,u\}$. Two rules govern the Roster method: if an element is repeated in the source description, it is written only ONCE in the set (repeats are never listed twice); and the ORDER in which elements are listed inside the braces is immaterial — $\{1,2,3\}$ and $\{3,1,2\}$ are the same set.

2. SET-BUILDER or Rule method: instead of listing every element, we describe the elements by stating the property that determines them uniquely, in the form $\{x / \text{property that } x \text{ satisfies}\}$. For example, $Y=\{\text{Jan, Feb, }\ldots\text{, Dec}\}$ can be written as $Y=\{x/x \text{ is a month of a year}\}$; and $B=\{1,4,9,16,25,\ldots\}$ can be written as $B=\{x/x\in N \text{ and } x \text{ is a square}\}$. …