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# Sets for Edexcel A-level Maths 1. Set notation
2. Combinations of sets
3. Venn diagrams

Set notation is used to list numbers and outcomes using curly brackets {}. The universal set, denoted as ξ, includes all the relevant values. Given a set A and an element of it a, a ∈ A states that a is an element of A. If every element in a set A is also an element of set B, set A is said to be a subset of set B, A ⊆ B. Given two sets A and B, A∩B represents the intersection between the two sets, A∪B represents the union between the two sets and A' represents everything not in set A. Venn diagrams are a diagram that groups different sets. The box the venn diagrams are placed in represents the universal set. The circles inside the box represent the different sets. Circles within each other represent subsets and overlapping circles represent the intersection between sets. The numbers on Venn diagrams can either represent the number of values in a set or the actual values. The following formula can be used to find the missing values in a Venn diagram: P(A∪B) = P(A) + P(B) − P(A∩B). # 1

Set U is {10, 11, 12, 13, 14, 15} and set V is {5, 10, 15}. State U∩V.

U∩V = {10, 15}. # 2

Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} and B = {2, 4, 6, 8, 10, 12, 14, 16}. Draw a Venn diagram to represent this data.

image # 3

A set X is defined as {2, 3, 4, 5, 6, 7}. State whether 8 ∈ X.

8 is not an element of the set, therefore 8 ∈ X is false. # 4

How can subsets be represented in Venn diagrams?

A circle drawn within a circle shows that the inner circle is a subset of the outer circle. # 5

What is the universal set of outcomes when rolling a die?

{1, 2, 3, 4, 5, 6} End of page