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Sets

Maths: Edexcel A Level Pure Maths, topic 1.2.1

Sets of Objects

Sets

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

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

Empty set

  • The symbol ∅ is used to the empty set: the set that contains no elements.
Notation

Notation

  • If an element e is in a set A, we write:
  • e∈Ae \in A
  • If an element d is not in A, we write:
  • d∉Ad \notin A
Using rules

Using rules

  • To define a set A using a rule, we can use the following notation:
  • A=A = {x:x2=4x: x^2 = 4}
  • Where {x:...x:...} means 'all values of xx such that'.
  • This means the set A has the elements {-2, 2}.
Number of elements

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.

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}?

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