Type in sizes for the sets A and B (maximum is 20) and hit Go! to generate new A and B sets. U is taken to be the set {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}.

Source code for BasicSetApplet (html version)

Further Questions

1. There are many relationships between the sizes of the following sets: A, B, A U B, A ^ B, and A - B. Find the relationships between the following:
(a) A \/ B and A /\ B
(b) A - B and A /\ B

2 (a) Can you derive an algorithm to compute B-A? Bc?
(b) Implement this in Java by extending this applet.

3. This applet demonstrates concepts that can be visualized using Venn Diagrams. For each set operation, draw a Venn diagram to convince yourself that the relationships you found earlier actually hold.

Note: Venn diagrams cannot be used in a formal proof!

Created by Andrew Freed, on January 30, 2002.
Modified by Andrew Freed, on April 15, 2002.

Development of this applet was sponsored by the Penn State Fund for Excellence in Learning and Teaching (FELT), project "Java-based Teaching of Mathematics in Information Sciences and Technology", supervised by Frank Ritter and David Mudgett.