Set-Notation-And-Venn-Diagrams Wjec-Eduqas Foundation

Set notation

What is a set?

• A set is a collection of elements

  • Elements could be anything

    • Numbers, letters, coordinates, …

• You could describe a set by writing its elements inside curly brackets {}

  • {1, 2, 3, 6} is the set of factors of 6

• If the set of elements follow a rule then you can write this using a colon inside the curly brackets {… : …}

  • The bit before the colon is the type of element

  • The bit after the colon is the rule 

    • {x is a positive integer : x² < 30} is the set of positive integers which, when squared, are less than 30

    • This is equal to {1, 2, 3, 4, 5}

  • The colon is often read as ‘such that’ 

  • If no type is specified, x can take any value (fractions, decimals, irrationals, …)

    • {x: x² < 30} means any value whose square is less than 30

  • A colon can also be replaced by a vertical bar

    • {x | x² < 30}

What do I need to know about set notation?

• is the universal set (the set of everything)

  • For example, if we are only interested in factors of 24 then = {1, 2, 3, 4, 6, 8, 12, 24}

  • You may see alternative notations used for  

    • U is a common alternative (different to for union!)

    • S or the Greek letter ξ (xi) may also be seen

• We use upper case letters to represent sets (A, B, C, …) and lower case letters to represent elements (a, b, c, …)

• n(A) is the number of elements in set A

  • For example, if  = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A  = {1, 4, 9}, B = {1, 2, 3, 4, 5, 6}
    n(A) = 3, n(B) = 6

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