What is a Venn Diagram?Date: 02/26/98 at 09:59:57 From: Chris B. Subject: Venn Diagrams What is a Venn Diagram? What is its use, definition, and what does it look like? Date: 02/26/98 at 14:38:32 From: Doctor Rob Subject: Re: Venn Diagrams A Venn Diagram is a picture that is used to illustrate intersections, unions, and other operations on sets. For one set A, it is represented by the points inside a circle in a plane. The complement of A is the points outside the circle, and in the plane. The Venn Diagram looks like a circle, with the letter A inside, near the edge. It divides the plane into two regions. For two sets A and B, each is represented by the points inside a circle in one plane. The circles are made to overlap. One is labeled A, the other B. The points inside one circle represent A, and those outside are the complement of A. The points inside the other circle represent B, and those outside are the complement of B. The overlap of the two circles is the intersection of A and B. All points inside either circle forms the union of A and B. The two circles divide the plane into four regions. To add a third set C, add a third circle which partially overlaps all four regions of the preceding diagram. The three circles divide the plane into eight regions. You cannot add a fourth circle to represent a fourth set D, but you can use a more complicated simple, closed, smooth curve for the same purpose. The interior of this curve must partially overlap all eight regions mentioned in the preceding paragraph. The four curves divide the plane into 16 regions. This can continue, but the diagram becomes quite unwieldy. A Venn Diagram is often used to illustrate the truth or falsity of statements in symbolic logic. The sets are the values of the variables. Set A represents variable a being true, and its complement represents a being false. Likewise for set B and variable b, set C and variable c, and so on. "a and b" is represented by the intersection of A and B, for example. -Doctor Rob, The Math Forum Check out our web site http://mathforum.org/dr.math/ |
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