Sets
Maths: Edexcel IGCSE Higher, topic 1.5.1
Sets of Objects
Sets
- Sets are collections of objects.
- The objects in a set are called its elements.
- A set is written using curly brackets:
- {2,3,4} is the set containing 2,3,4
- {positive even numbers below 5} = {2,4}
Universal set
- The symbol ξ is used for the universal set: the set that contains everything.
- On a Venn diagram, ξ is everything inside the rectangle.
- The "complement of a set A" is written as A’
- It is the set of all the things that aren’t in A.
Empty set
- The symbol ∅ is used to the empty set: the set that contains no elements.
Notation
- If an element e is in a set A, we use the following notation:
- If an element d is not in A, we use the following notation:
Number of elements
- The number of elements in a set A is written as n(A).
- In the example shown here, n({2,3,4}) = 3.
Subsets
As we have seen previously, the universal set contains all elements, and can also contain sets. We say that these sets are subsets of the universal set.
Subsets
- Subsets are sets contained within other sets.
- The set A is a subset of set B if all of the elements in A are also elements in B.
- For example the set A = {2, 3, 4} has the following subsets:
- {2, 3}, {3, 4}, {2, 4}, {2}, {3}, {4}, {2,3,4}
- Every set is its own subset.
Notation
- If A is a subset of B, we write:
- A ⊂ B
- If C is not a subset of B, we write:
- C ⊄ B
Test yourself on Sets
What is the symbol for the universal set?
Which of these are contained in the set {odd numbers}?
Which of these are contained in the set {square numbers}?
Which of these are contained in the set {less than 5}?
Which of these are contained in the set {more than 5}?