Introduction to Sets
Elements • Notation • Relationships
A set is a well-defined collection of objects or things. The objects inside a set are called its elements or members.
Sets are usually named with capital letters such as \( A, B, C \), and elements are written inside curly brackets: \( A = \{1, 2, 3, 4\} \).
- 1 \( a \in A \) means \(a\) is an element of set \(A\)
- 2 \( b \notin A \) means \(b\) is not in \(A\)
- 3 The cardinal number is the number of elements in the set
Examples
\( A = \{1, 2, 3, 4, 5\} \)
Set of numbers from 1 to 5
\( B = \{\text{red}, \text{blue}, \text{green}\} \)
Set of colours
\( 3 \in A \), \( 6 \notin A \)
Membership notation
\( A \subseteq U \)
\(A\) is a subset of the universal set \(U\)
