Sets

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Definitions

Natural Numbers (N) - Any positive whole number

Integers (Z) – Any positive or negative whole number

Multiples – The different numbers one number divided into(example; multiples of 2 are 2, 4, 6, 8..., because 2 divides into all of those numbers)

Factors – Numbers that divide evenly into another number

Inclusive – To include (example: the numbers 1 to 5 inclusive will include 1 and 5)

Sets

A set is a collection of things.

e.g. clothing, sports, people, numbers,

Sets in numbers

Usually, we are asked to deal with groups of people or sets of numbers

e.g.

Set A is the days of the week

Set B is the even numbers from 1 – 10

How would we list these as sets?

Set A =

Set B =

Venn Diagrams

These are visual diagrams representing information. Each circle represents a set. When someone is part of more than one set we create an overlap to allow them be in both circles.

A set is a collection of numbers or objects.

A picture called a Venn diagram is used to represent sets and show the relationship between them.

Venn diagrams can also be used to show the number of members in a set.

The universal set is the set of elements from which members of all other sets are selected. The symbol  is used to represent the universal set.

A’ is called the complement of set A. A’ contains all the members of  that are not in set A.

The symbol  is used to represent the empty set.   {} The symbol  is used to represent the intersection of two sets. A  B is the set of members of  that are in both set A and set B

The symbol  is used to represent the union of two sets. A  B is the set of members of  that are in set A or in set B or in both sets

? ∩ ? A intersection B What is common to both

? ∪ ? A union B List all the elements in A and all the elements in B

?′ A complement List everything outside of A

?∖? A difference B List the elements in A without any of B

#? The cardinal number of A How many elements are in A

? ⊂ ? A is a subset of B Everything in A is also in B.

∈ 'Is an element of’

These symbols can be combined.

(? ∩ ?)′ Everything outside of A intersection B

? ∪ ? ∖? All of A and all of B but don’t list any elements of C