Complements, Unions, and Intersections of SetsDate: 10/13/2004 at 18:45:57 From: Turtle Subject: Universal sets How do you shade in the complement, union, and intersection? I tried to look it everywhere up but I got so frustrated. Date: 10/13/2004 at 22:23:28 From: Doctor Peterson Subject: Re: Universal sets Hi, Turtle. I suppose you are asking about problems where you are given a Venn diagram, perhaps of two sets, or perhaps more, and are told to shade various sets such as the complement of one set, the union of two sets, or the intersection of two sets. Think about the meaning of each term. The complement of a set is everything EXCEPT that set. So if you have a set shown inside a universal set (a larger set that is thought of as containing all the objects under consideration), just shade in the OUTSIDE of the given set--everything in the universal set that is NOT in that set: +---------------------+ +---------------------+ | | |:::::::::::::::::::::| | +---------+ | |:::::+---------+:::::| | / \ | |::::/ \::::| | / \ | |:::/ \:::| | + + | |::+ +::| | | | | |::| |::| | | A | | |::| |::| | | | | |::| |::| | + + | |::+ +::| | \ / | |:::\ /:::| | \ / | |::::\ /::::| | +---------+ | |:::::+---------+:::::| | | |:::::::::::::::::::::| +---------------------+ +---------------------+ set A complement of A inside universal set in the universal set The union of two sets is the set of all objects that are members of EITHER set; that is, it is the result of combining the sets, as if you poured the contents of two bags into a new one. To shade it in, shade in all of both sets: +---------------------+ +---------------------+ | | | | | +-----+ | | +-----+ | | / \ | | /:::::::\ | | + + | | +:::::::::+ | | | A | | | |:::::::::| | | + +--+--+ | | +:::::::::+--+ | | \ / / \ | | \::::::::::::\ | | +--+--+ + | | +--+:::::::::+ | | | B | | | |:::::::::| | | + + | | +:::::::::+ | | \ / | | \:::::::/ | | +-----+ | | +-----+ | | | | | +---------------------+ +---------------------+ union of A and B The intersection of two sets is the set of all objects that are members of BOTH sets; it's the overlap between them. To shade that in, just shade in only the part that is inside both sets: +---------------------+ +---------------------+ | | | | | +-----+ | | +-----+ | | / \ | | / \ | | + + | | + + | | | A | | | | | | | + +--+--+ | | + +--+--+ | | \ / / \ | | \ /::/ \ | | +--+--+ + | | +--+--+ + | | | B | | | | | | | + + | | + + | | \ / | | \ / | | +-----+ | | +-----+ | | | | | +---------------------+ +---------------------+ intersection of A and B Here are some pages that discuss this: What is a Venn Diagram? http://mathforum.org/library/drmath/view/52420.html Sets: Unions and Intersections http://mathforum.org/library/drmath/view/52395.html If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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