DSC325-Lec3-A - STATISTICS FOR MANAGEMENT DECISIONS DSC 325...

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STATISTICS FOR MANAGEMENT DECISIONS DSC 325 – Lec3A A REVIEW OF SETS A SET is a collection of distinct objects called elements. Let V be a set of Roman vowels. Then V can be expressed as, V = {a, e, i, o, u} e is a member of V and this is expressed as e V t is not a member of V , and this is expressed as t V A SUBSET Let set V = {a, e ,i, o, u} . And let set W = {a, e, u} . Since all elements in set W also appear in set V , we conclude that W is a subset of V. This is expressed as W V In this case we say that W is a proper subset of V . Consider the following two sets. 1
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M = {1, 4, 5} and N = {4, 1, 5} Since every element in set M is also found in set N and vice versa, each set is contained in the other and this is expressed as: M N and N M Consider the following sets A, B, C. It can be easily seen that: A A And if A B and B C , then A = B And if A B and B C , then A C Consider the following sets: J = {1, 2, 3, x ,y} K = {3, 4, y, z} and L = {n, y, 2, z} It can clearly be seen that: J K, K J, J L L J, K L, and L K None of these sets is a subset of the other. A UNIVERSAL SET or THE UNIVERSE Let V = {a, e, i, o, u} . Since set V contains all the Roman vowels, we refer to set V as the universal set or the universe of Roman vowels. 2
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A COMPLEMENT Let V be the universe of Roman vowels. Then, V = {a, e, i, o, u} . Now consider a set W = {a, e, i} . Since all elements in set W are members of set V but not vice-versa, Set W is a proper subset of set V. W V . The complement of set W which we denote as W (pronounced as w prime), or W C ( pronounced complement of W ) is itself a set that consists al
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