Universal set and subsets: a Venn diagram
The universal set is the numbers 1 to 12. Choose two sets from it, see their members in a Venn diagram, and find out when one set is a subset of the other.
Core concept
The universal set U holds every member we are talking about; A is a subset of B (A ⊆ B) when every member of A is also in B, and the complement A′ is everything in U that is not in A
Topic: Sets
When we talk about sets, we first agree on everything we are talking about: the universal set, U. Here U = {1, 2, 3, …, 12}, drawn as a rectangle. Sets inside it are drawn as circles. If every member of A is also a member of B, then A is a subset of B, written A ⊆ B. For example, every multiple: What you get when you multiply a number by 1, 2, 3 … 12 is a multiple of 3. All key words of 4 is even, so {4, 8, 12} ⊆ {2, 4, 6, 8, 10, 12}. The members that are in both A and B form their intersection, A ∩ B. The members of U that are not in A form the complement of A, written A′, so n(A′) = n(U) − n(A).
What you will learn
- Define a universal set and show it in a Venn diagram.
- Decide whether one set is a subset of another.
- Find the intersection of two sets.
- Find the complement of a set in the universal set.
Before you start
- Know how to list the members of a set.
Materials
- Number cards from 1 to 12, two hoops or circles of string
Equipment
- None
Procedure
- Record A = multiples of 4 and B = even numbers.
- Swap them: A = even numbers and B = multiples of 4, and record.
- Record A = prime numbers and B = multiples of 3.
How this simulation is simplified
- The universal set is U = {1, 2, 3, …, 12}.