The Venn diagram is a graphical way to represent sets and set operations. Each diagram begins with a rectangle illustrating the universal set. Then each set is represented by the interior of a circle, square, or other shape.
Below are Venn diagrams for the set a, shaded in yellow, and for the complement of a, everything in U that is not in a.
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| Venn diagram for set a | Venn diagram for set a' |
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The inhibition operations "a, but not b" and "b, but not a" are clearly not commutative, as shown by their Venn diagrams below
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The exclusive or operation, "a or b, but not both", is clearly commutative from the symmetry of its Venn diagram.
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A Venn diagram ideally should have a separate region for each minterm. For n variables, there are 2n minterms. They are typically listed in a truth table.
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| Venn diagram regions | truth table |
Maintained by John Loomis, last updated 30 May 2004