About Venn Diagrams

Venn (or set) diagrams are used to illustrate set relations. In this applet, the three intersecting circles each represent a set of elements, contained in some universe of elements depicted by the rectangle.

Using the Applet

This applet lets you practice filling in a Venn Diagram to represent a given set. The following table explains the notation you'll see:

Symbol Name Definition
\( X \cup Y \) Union The set of all elements in either X or Y
\( X \cap Y \) Intersection The set of all elements in both X and Y
~\(X\) Complement The set of all elements that are not in X
\(X - Y\) Set Difference The set of all elements in X but not in Y (equivalent to X ∩ ~Y)
Empty Set The set containing no elements

For instance, the diagram below represents the set \( (A \cup C) - B \), because it contains all of the elements that appear in either \(A\) or \(C\), but not in \(B\):
Click the regions of the diagram that correspond to the set shown. You'll see a message of "Correct" when you've found all of the regions included in the set, without any extras. Click the "New Set" button to generate the next set. The colors of the regions have nothing to do with the sets - they are simply the result of subtractive color mixing.

Don't forget about the universal elements that are not contained in \(A\), \(B\), or \(C\). Click inside the rectangle, but not inside any of the circles, if your set includes elements in the complement of \(A \cup B \cup C\).

About this Applet

This applet was created using JavaScript and the Raphael library. If you are unable to see the applet, make sure you have JavaScript enabled in your browser. This applet may not be supported by older browsers.