# BasicSetApplet

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}.

## 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, arf132@psu.edu on January 30, 2002.
Modified by Andrew Freed, arf132@psu.edu 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.