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.

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

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 \(B\):
var samplepaper = new Raphael(document.getElementById('samplebox'), 200, 200);
var Ashade = samplepaper.circle( 70, 70, 60 ).attr({"stroke":1, stroke: '#666',"fill":"gray","fill-opacity":0.4})
var Cshade = samplepaper.circle( 100, 130, 60 ).attr({"stroke":1, stroke: '#666',"fill":"gray","fill-opacity":0.4})
var Bcircle = samplepaper.circle( 130, 70, 60 ).attr({"stroke":1, stroke: '#666',"fill":"white","fill-opacity":1})
var Acircle = samplepaper.circle( 70, 70, 60 ).attr({"stroke":1, stroke: '#666',"fill":"gray","fill-opacity":0})
var Ccircle = samplepaper.circle( 100, 130, 60 ).attr({"stroke":1, stroke: '#666',"fill":"gray","fill-opacity":0})
var Asampletext = samplepaper.text(40, 60, "A").attr({'font-size': 18}).attr("fill", "#666");
var Bsampletext = samplepaper.text(160, 60, "B").attr({'font-size': 18}).attr("fill", "#666");
var Csampletext = samplepaper.text(100, 150, "C").attr({'font-size': 18}).attr("fill", "#666");
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 \(A \cup B \cup C\).

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 \(B\):

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 \(A \cup B \cup C\).

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.