Equal, subset, overlapping or disjoint sets?
List twelve pairs of sets, from the letters of “follow” and “wolf” to the factors of 12 and 18. Find their members in common, compare how many members each has, and sort the pairs by how the sets are related.
Core concept
Two sets can be equal (the same members), one can be a proper subset of the other, they can overlap (some members in common) or be disjoint (none in common); sets with the same number of members are equivalent, even if their members differ
Topic: Sets
A set can be written in three ways: by description (“the factor: A number that divides another exactly. 3 is a factor of 12. All key words of 6”), by listing its members ({1, 2, 3, 6}), or in set-builder form ({x : x is a factor of 6}). Two sets can be related in four ways. They are equal (A = B) if they have exactly the same members, in any order. A is a proper subset of B (A ⊂ B) if every member of A is in B but B has more members. They are overlapping if they share some members but neither is inside the other. They are disjoint if they have no members in common. Sets are equivalent if n(A) = n(B), the same number of members, even when the members differ: equal sets are always equivalent, but equivalent sets need not be equal.
What you will learn
- Write a set by description, by listing and in set-builder form.
- Decide whether two sets are equal, a proper subset, overlapping or disjoint.
- Tell equal sets from equivalent sets.
- Show the relation between two sets in a Venn diagram.
Before you start
- Know set notation and the types of sets.
Materials
- A notebook to list the sets and draw Venn diagrams
Equipment
- None
Procedure
- Pick a pair of sets and list both.
- Find their members in common and compare n(A) and n(B).
- Do this for at least eight pairs, then sort them all.