### Subsets and Proper Subsets

Check out Bas Rutten's Liver Shot on MMA Surge: http://bit.ly/MMASurgeEp1 Mahalo math expert Allison Moffett teaches viewers about subsets and proper subsets. Sample Set --------------------------------------------------------------------- Set A contains the elements a, b and c. Subsets --------------------------------------------------------------------- A subset is either all of the elements of a set or just some of the elements. This is its mathematical symbol:??.Because b and c are elements of set A, {b,c}?? A.Because a, b and c are in set A, {a,b,c}???A. Example --------------------------------------------------------------------- B = {1,2,6,8}{1,8,6}?? B{8,6,2,1}?? B Proper Subsets --------------------------------------------------------------------- A proper subset is a subset that contains some, but not all, of the elements of the original set.?This is its mathematical symbol:??.{b,c}?is a proper subset of set A, because one of set A's elements is missing.?{b,c}???A.?{a,b,c} is not a proper subset of set A, because it contains all of set A's elements. Example --------------------------------------------------------------------- B = {1,2,6,8}{1,8,6}???B{8,6,2,1} is not a proper subset. Empty Sets --------------------------------------------------------------------- If a set has no elements in it, it is an empty, or null, set, shown as ?. This is an empty set: { }.Because an empty set contains no elements, it is a subset of all sets.The logic behind this is that because there are not any elements in the empty set that are not in any given set, it must be true that all elements in the empty set are in any given set.Because an empty set does not contain the elements of any set but itself, it is a proper subset of every set but itself.c Example --------------------------------------------------------------------- B = {1,2,6,8}B?≠ {3,4}{ } ≠?{3,4}{ } ? B{ } ? B{ } is not a proper subset of?{ }. Read more by visiting our page at: http://www.mahalo.com/subsets-and-proper-subsets/

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