What is set notation?

• Set?notation?is a formal way of writing groups of numbers (or other mathematical entities such as shapes) that share a common feature – each number in a set is called an?element?of the set
  • You should have come across common sets of numbers such as the?natural?numbers, denoted by ?, or the set of?real?numbers, denoted by
• In?probability, set notation allows us to talk about the?sample?space?and?events?within in it
  • S, U, , ?are common symbols used for the Universal set
    In probability this is the entire sample space, or the rectangle in a?Venn diagram
  • Events?are denoted by capital letters,?A, B, C?etc
  • The?events are denoted by ?etc
    (Strictly pronounced “A? prime” but often called “A? dash”)
    is called the?complement?of?A
• In probability we are often looking at combined events
  • The event?A?and?B?is called the?intersection?of events?A?and?B?, and the symbol ∩ ?is used
    i.e.??A?and?B ?is written as
    • On a?Venn?diagram?this would be the?overlap?between the bubble for event?A?and the bubble for event
    • From?Basic?Probability, for?independent?events

• • 
  • The event A or B is called the union of events A and B , and the symbol∪?is used
    i.e. ?A or B??is written as
    • On a?Venn?diagram?this would be?both?the bubbles for event A and event B including their?overlap?(intersection)
    • From?Basic?Probability, for?mutually?exclusive?events

• • 
  • The other set you may come across in probability is the?empty?set
    The empty set has no elements and is denoted by

The?intersection?of?mutually?exclusive events is the empty set,

• And finally,

How do I solve problems given in set notation?

• Recognise the notation and symbols used and then interpret them in terms of?AND (∩),?OR (∪) and/or?NOT?(‘) statements
• Venn diagrams lend themselves particularly well to deducing which sets or parts of sets are involved- draw mini-Venn diagrams and shade them
• Practice shading various parts of Venn diagrams and then writing what you have shaded in set notation
• With combinations of?union,?intersection?and?complement?there may be more than one way to write the set required
  • e.g.?

    Not convinced?? Sketch a Venn diagram and shade it in!

  • In such questions it can be the?unshaded?part that represents the solution