Venn Diagrams and de Morgan's Laws 1

Probability - Venn diagrams 1, for 2 events, and de Morgan's Laws. This applet does not specifically state de Morgan's Laws, but by investigation of relationships in Venn Diagrams they can be deduced. Play around with this applet and the Laws become almost obvious!

Author and programmer: Ron Barrow

UK Years 12-13, Ages 16-19, KS2, KS4, AS and A Level Statistics and Probability, Set Theory
US Grades 11, 12, Statistics and Probability, Set Theory

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Instructions below    See also: Venn diagrams 2

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How to Use this Applet

On the screen you will see two overlapping circles, A and B, drawn inside a rectangle. This is a simple example of a Venn diagram, named after the British logician John Venn, 1834-1923.
Use the drop-down menu at the top of the page to choose a logical region, and you will see that region appear in red on the Venn diagram.
You can move the circles by clicking their centres and dragging with the mouse. In this way you can see what happens when the circles are separated or have a different overlap.

If you're completely new to the subject, see if you can follow what's going on just from trying different regions. If you have some knowledge of this subject, I hope that this applet will help you to master it.
Later on you might want to investigate which regions are the same despite having different description; in this way you may discover the very important de Morgan's Laws for yourself! Augustus de Morgan, 1806-1871, was another British mathematican and logician.
Play around. Enjoy yourself!