SETS -
A set is a well-defined collection of objects. By ‘well defined’ we mean that it must be possible to tell beyond doubt whether or not a given object belongs to the collection that we are considering.
For example, the following are well defined collections and so are example of sets
(i) The set of numbers 1, 3, 5, 7, and 10.
(ii) The set of students of your drawing class
The following does not describe a well-defined collection and so are not sets –
(i) The vegetables which taste good to all. People may have different tastes.
(ii) All good movies. People may have different likings.
Members of a set and symbol for ‘Belongs To’ –
The objects that belong to a set are called members of elements of the set. The Greek letter ‘epsilon’ ∈ is used for understanding ‘belongs to’.
For Example –
a ∈ {a, b, c},
b ∈ {a, b, c},
c ∈ {a, b, c},
we also say that, ‘a’, ‘b’, ‘c’ are included in the set.
The symbol ∉ is used to mean ‘is not a member of’.
Thus 1 ∉ {0, 2, 4, 6}
Note – The braces { } are used to enclose the members of a set
Representation of a Set –
Capital letters, e.g., A, B, S etc., used to name sets. There are three ways of representing a set.
(1) In words:- We can use words to describe a set, e.g., the set of multiples of whole numbers less than 10.
(2) Roster or Tabulation Method,
(3) Rule Method or Set Builder Method,