I made mention of Venn diagrams in this week’s podcast. These are simple diagrams that can be used to map formal logic statements such as:
In this Venn diagram, the circle labeled “Collies” is completely contained within the circle labeled “Dogs” so that there cannot be anything that is a Collie that is not a Dog. So this diagram illustrates the logical statement “All collies are dogs.”
In this second simple Venn diagram, the circle labeled “Cats” is completely outside the one labeled “Dogs” so that anything that falls into the category of Cats (and can thus be included in the Cats circle) will fall completely outside the category of Dogs. So this diagram illustrates the logical statement “No cats are dogs.” (Note: I kept Collies inside the Dog circle to illustrate that a Venn diagram can illustrate more than one logical statement. In this case, the second statement is “No cats are collies.”)
You can also use Venn diagrams to map out more complex statements, or statements that cover some vs. all of the things that fall into a category. For example:
This diagram illustrates the statement “Some accountants are women.” In this case, the circle labeled “Accountants” and the one labeled “Women” overlap, but do not completely enclose one another. So this diagram actually covers two statements: “Some accountants are women” and “Some women are accountants.”
Getting back to dogs and cats, this final Venn diagram shows how all cats can be animals and all dogs (including collies) can be animals, while still preserving the notion that no cat can be a dog. As you can see, the “Dogs” and “Cats” circles are completely enclosed inside the “Animals” circle (which illustrates that anything that is a cat or a dog must be an animal), while preserving the notion that no cat can be a dog (and vice versa).
While these are simple examples, Venn diagrams can get quite intricate as they start to illustrate more complex statements and arguments. Here are some resources you can turn to if you want to explore Venn diagrams further:
http://www.purplemath.com/modules/venndiag.htm
Video Lesson: http://www.youtube.com/watch?v=a3Cme7wUBhg
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