Subsets and Proper SubsetsDate: 07/10/98 at 20:47:49 From: Melinda Dwelly Subject: Subsets I don't understand the difference between subsets and proper subsets. Please explain and give examples. Thank you. Melinda Dwelly Date: 07/11/98 at 02:06:00 From: Doctor Mike Subject: Re: Subsets Dear Melinda, If every member of one set is also a member of a second set, then the first set is said to be a subset of the second set. Usually, it turns out that the first set is smaller than the second, but not always. The definition of "subset" allows the possibility that the first set is the same as (equal to) the second set. But a "proper subset" must be smaller than the second set. Example 1: The set {2,3,5,7} is a subset of {2,3,5,7}. The set {2,3,5,7} is NOT a proper subset of {2,3,5,7}. The set {2,3,5} is a proper subset of {2,3,5,7}. Example 2: It is possible to specify sets in different ways. A = {0,1,2,3,4,5,6,7,8,9} means the set of all digits. A = {0,2,4,6,8,1,3,5,7,9} means exactly the same thing. B = {D | D is a digit in Bill Clinton's phone number, including the area code} has exactly the digits of the President's phone number. You know that B must be a subset of A, because everything in B is a digit, and every digit is in A. But is it a proper subset? The answer is yes because the area code in Washington D.C. is 202, so his number is of the form 202/abc-defg, and if you put all of the digits of that phone number in a set you have at most nine members, which is less than the size of set A. But if C is the set of digits in Bill Clinton's phone number back in Arkansas when he was the governor, then it gets more complicated. The area code for all of the state of Arkansas is 501. So, C could be a proper subset of A or not. Let's look at 2 possibilities. If his phone number was 501/555-1212, then the set C would be {0,1,2,5}. However, if his phone number was 501/234-6789, then set C would be {0,1,2,3,4,5,6,7,8,9} which is not a proper set of A. I hope this helps. - Doctor Mike, The Math Forum Check out our web site! http://mathforum.org/dr.math/ Date: 09/18/2001 at 15:03:55 From: Dan Subject: Sets What is a proper subset? I think when two sets are identical, then you can say one is the proper subset of the other, but I'm not sure if I'm right. Date: 09/18/2001 at 17:35:27 From: Doctor Jodi Subject: Re: Sets Hi Dan, Do you know what a subset is? A PROPER subset is any subset of a set EXCEPT ITSELF. So for instance, if you start with the set {Green Eggs, Ham, Cheese}, {Ham, Cheese} is a proper subset, but {Green Eggs, Ham, Cheese} is NOT a proper subset. Hope this helps! - Doctor Jodi, The Math Forum http://mathforum.org/dr.math/ |
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