#### Set Language and Notation

- A well-defined collection of objects is called a
*set*and each object is called a*member*or*element*of the set - A set is denoted by a capital letter and is expressed by:
- Listing its elements, e.g. V = {a, e, i, o, u}, or
- A set builder notation:
- R – set of real numbers
- R
^{+}– set of positive real numbers - N – set of natural numbers
- Z – set of integers
- Z
^{+}– set of positive integers - E.g. {x: x is a prime number and x < 30}

- For any finite set P, n(P) denotes the number of elements in P
- A null or empty set is denoted by {} or ø
- For any two sets P and Q:
- P = Q if they have the same elements
- P ⊆ Q if x ∈ P ⇒ x ∈ Q
- P ∩ Q = {x: x ∈ P and x ∈ Q}
- P ∩ Q = ø then P and Q are disjoint sets
- P ∪ Q = {x: x ∈ P or x v Q}

- For any set P and universal set ξ
- P ⊆ ξ and 0 ≤ n(P) ≤ n(ξ)
- P’ = {x: x ∈ ξ and x ∉ P}
- P ∩ P’ = ø
- P ∪ P’ = ξ