Basic Set Theory

Feb 3rd, 2012
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This guide on Basic Set Theory Is easy to understand and uses familiar everyday examples to explain the concepts of intersection, union and complement of a set. Examples with solutions are then given. Venn diagrams are drawn to give another way of understanding the concepts. The guide ends with some more difficult solved examples of the kind often set in examinations.

Word Count: 1540
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Basic Set TheorySets are written in curly brackets with a comma between each member or element inside. To make it easy to grasp the concepts, we will work in a familiar setting - the school. Suppose there are 11 students in the whole school. Let us call them a, b, c, d, ?k. In set notation we write this as : U= {a,b,c,d,e,f,g,h,i,j,k}The letter capital U usually stands for the universal set because it is the universe or total of all the students in our school - there are no more. Also, the order of writing the elements does not matter.There are 11 elements or members in this universal set (we would call them students if we were outside the mathematics class). A subset of U (or simply a set in U) is just a set with some of the members we use (capital) letters for them. Three sets are shown below.A={a,b,c,d,e}B= {c,d,e,f}C= {h,i,j}Now we will define three operations on these sets. Operations are just a way of combining the sets.Consider A?B (read as A intersect B)The intersection of two sets is simply the set containing all the elements common to both.Hence A?B = {c,d,e}We could also write {a,b,c,d,e}?{c,d,e,f} = {c,d,e}Now suppose set A represents the members of the football team and B represents the rugby team. The headmaster wants to see all members of the football team and all members of the rugby team in his office immediately. Who should go? Obviously a,b,c,d,e,f should all go.We represent this situation as A? B (read as A union B)The Union of two se

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