1. Sets & venn diagrams; probability

2. A B AB Venn diagrams set = collection of things
Circle diagram displaying 2 or more sets
Easy to identify “overlaps” use “curly brackets” to list a set
Example of sets
A = {1, 2, 3, 4, 5, 6, 7} = set of first 7 counting numbers
B = {1, 2, 3, 4, 6, 12} = set of factors of 12
C = {3, 6, 9, 12, 15, …} = set of multiples of 3
This set continues indefinitely, label each set using a capital letter as indicated by “…”
Eg A, B, C etc So the multiples of three form an infinite set.
Jayne Bullock 2012

3. A B 4 6 8 3 5 7 2 9 Venn diagram example
Consider the set consisting of the following numbers: {2, 3, 4, 5, 6, 7, 8, 9} Circle A = even numbers Circle B = prime numbers The separation of even numbers and prime numbers is easy to identify. A B 4 6 8 3 5 7 2 9
Jayne Bullock 2012

4. A B AB C AC BC ABC Venn diagrams
Venn diagrams need not consist of only two circles {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Circle A = even numbers; Circle B = multiples of 3; circle C = factors of 12 A B AB C AC BC
ABC
Jayne Bullock 2012

5. Venn diagrams
Venn diagrams need not consist of only two circles {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12} Circle A = even numbers; Circle B = multiples of 3; circle C = factors of 12 A B 10 8 9 C
2 4 3
6 12 1 11 5 7
Jayne Bullock 2012

6. definitions
Element or Member Each item in a set is called an element or a member of the set n(A) or n|A| The number of elements in set A. Eg: n(A) = 5 The number of elements in A is 5 a ∈ C a is an element of C. b ∉ C b is not an element of C. {a, e, i} ⊂ C The set {a, e, i} is contained in set C. The order that we list the elements of a set is unimportant, however it is often convenient to list sets in alphabetical or numerical order. If a set has no elements it is said to be empty: ∅. Eg {multiples of 4 that are odd numbers} = ∅.
not
Jayne Bullock 2012

7. The universal set, Intersection, union and complement
The universal set: U The set containing all of the elements under consideration. In Venn diagrams we draw a box around the circles and this box represents the universal set for that situation. Intersection: ∩ The overlap between two sets. Union: ∪ The combination of the elements of one set with the elements of another set. Eg: C = {1, 2, 3, 4} D = {2, 4, 6, 8} ∴ C∪D = {1, 2, 3, 4, 6, 8} ∴ C ∩ D = {2, 4} Complement: A’ (A dash) or Ā (A bar) Everything lying in the universal set but lying outside set A. U A B AB
Jayne Bullock 2012

8. Venn diagrams using notation