Sorting Disjoint Sets and Intersecting Sets
Definitions
Disjoint sets
Disjoint sets are sets that share no common elements, meaning their intersection is the empty set, while intersecting, or overlapping, sets share at least one common element.
Disjoint sets are independent/mutually exclusive, while intersecting sets share an overlap.
Disjoint Sets
Definition: Two sets, A and B, are disjoint if (A &union; cap B = emptyset) (A intersection B equals empty set).
Key Property: They have absolutely no elements in common.
Venn Diagram: Represented as two separate, non-overlapping circles.
Example: Set (A = {1, 2, 3}) and Set (B = {4, 5, 6}).
Since they share no numbers, they are disjoint.
Real-world Example:
The set of prime numbers and the set of even numbers greater than 2.
Intersecting Sets (Overlapping Sets)
Intersecting Sets (Overlapping Sets) are sets that share at least one element.
Key Property: Their intersection is not empty, meaning (A intersection B is not an emptyset).
Venn Diagram: Represented by two circles that overlap, showing the common elements in the intersection region.
Example: Set C = {1, 2, 3} and Set D = {3, 4, 5}.
Are intersecting because they share the element {3}.
Real-world Example: A set of musicians and a set of teachers someone can be both.
Task 1
- Sort the objects into groups.
- Explain what you are doing.
- Put yarn around the groups and explain how you decide to put the yarn.
- Response
- Sorts objects into groups according to one property for each object (all yellow, all blue… or squares, circles…). Uses the category of "other".
- Sorts objects into groups according to two properties for one object (big squares, little squares…).
Task 2
- Sort the objects another way?
- Put yarn around two categories that are completely different
- Response
- Sorts objects into unique groups.
- Sorts objects by one property (color).
- Sorts objects by two properties (color and shape).
- Sorts objects by three properties (color, shape, size).
Task 3
- Form the yarn so that there are two circles that overlap.
- Put an object in one of the circles.
- Put another object into the other circle.
- Can you find something that could fit in both circles.
- If so, where would it go?
- If not, can you change the groups so they could.
Responses
- Sorts objects into unique groups.
- Identifies objects by using more than one property.
- Sorts objects by using more than one property.
- Sorts objects by using intersecting groups.
Tasks Summary
Lower level
- Can sort by one property
- Can sort by two properties.
- Can sort by three properties.
- Can represent disjoint groups.
- Can represent groups that intersect.
- Can explain class inclusion.
Top level