Unions and IntersectionsDate: 9 Feb 1995 15:30:17 -0500 From: Priscilla Warren NWISD Subject: algebra HELP!!! I need to get help in Algebra. My question is about intersections and unions. In my text, there are these upside-down horseshoe looking things and there is no explanation of what they are or why they exist. If you could explain them to me it would be very helpful. And if you have any hints for passing Algebra, that would be great too. examples: (A U B) U C ( something like that) A={x l x >-1} ( a l represents a straight line) Thank you me now :( me after you bail me out :-} Paula e-mail: pfw@tenet.edu Date: 9 Feb 1995 15:55:53 -0500 From: Dr. Sydney Subject: Re: algebra Dear Paula: Hello! We are glad you wrote Dr. Math with your questions! Before we talk about what unions and intersections are, let's look at the context in which we use unions and intersections. We usually use them when talking about SETS. A set is really just a collection of objects, numbers, or whatever. For instance, the natural numbers are a set. Or, A in your example is a set. If we have two sets, A and B, then the union of A and B is notated: A U B. A U B is a new set whose elements are the elements of both A and B. So, if something is an element of either A or B, it is also an element of A U B. Suppose we have the sets: A = {real numbers xlx>0} (so, this is just the positive real numbers) and B = {yl y is an integer}. Then, A U B would be the set of positive real numbers and negative integers (0 is included). Now, the INTERSECTION of A and B is a little different. The usual notation for intersection is kind of an upside down U. If you take the union sign and flip it, you will get the intersection sign. But, since there is no such sign on the keyboard, I will use "i" to signify intersection. So A i B is a new set whose elements are in both A and B. So, in the example above, A i B would be the set of all positive real integers since positive real integers are in A (they are positive real numbers) and they are also in B (they are integers). Sometimes two sets have no elements in common. Then the intersection of the two sets is called the empty set, often denoted {}. For instance, if C = {1, 3, 5, ...} and D = {2, 4, 6, ...}, then C i D = {}. Let me just give one more example on a more finite level that might make things clearer. Suppose you have the following two sets: K={0,1,2,3,6,8} F={-1, 2, 3, 7/2, 8} Then K U F is the set of all numbers that are in either K or F. So, K U F = {0,1,2,3,6,8,-1,7/2} K i F is the set of all numbers that are in both K and F. So, K i F = {2,3,8} I hope this helps write back with any more questions you might have. Good luck with the algebra! --Sydney, "dr. math" |
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