Representation of Sets

Sets can be represented in two ways, one is known as the Tabular or Roster form and the other is famous as the Set-Builder form, these two forms can be used to represent the same data, just the style varies in both cases.

Roster Form

In Roster Form, the elements are inside { } Curly brackets. All the elements are mentioned inside and are separated by commas. The roster form is the easiest way to represent the data in groups.

For example, the set for the table of 5 will be, A= {5, 10, 15, 20, 25, 30, 35…..}.

Properties of Roster form of Sets:

• The arrangement in the Roster form does not necessarily have to be in the same order every time. For example, A= {a, b, c, d, e} is equal to A= {e, d, a, c, b}.
• The elements are not repeated in the set in Roster form, for example, the word “apple” will be written as, A= {a, p, l, e}
• The Finite sets are represented either with all the elements or if the elements are too many, they are represented as dots in the middle. The infinite sets are represented with dots at the end.

Set-Builder Form

In Set-builder form, elements are shown or represented in statements expressing relations among elements. The standard form for Set-builder, A= {x : statement}.

For example, A = {x : x ∈ N ^ x < 9}

Properties of Set-builder form:

• To write the set in Set- builder form, the data should follow a certain pattern.
• Colons (:) are necessary for the Set-builder form.
• After the colon, the statement is to be written.

Order of the Set

The order of the Set is determined by the number of elements present in the Set.

For example, if there are 10 elements in the set, the order of the set becomes 10. For finite sets, the order of the set is finite and for infinite sets, the order of the set is infinite.