11Avenn

= Venn Diagrams =


 * A set is a collection of elements (or things, people, activities, numbers, ideas, etc)


 * Sets are often named with capital letters: A, B, C, etc


 * n(A) represents the number of elements in the set called A.

A ** Venn Diagram ** is a way of representing one or more sets within the Universal Set.
 * A rectangle is used to denote the entire sample space (or the Universal Set)
 * The symbol ** E ** represents the universal set.
 * A circle inside the rectangle denotes a set (a subset of the Universal Set)
 * The circle may contain
 * the elements within that set, or
 * the number of elements within the set.


 * Example **
 * ** E ** = {1, 2, 3, 4, 5, 6, 7, 8}


 * A = {1, 3, 5, 7}


 * B = {1, 2, 3, 4}


 * Union (OR) **
 * The Union of two sets is A ** È **B


 * It includes all elements that are in __**either**__ A __**or**__ B.


 * A ** È ** B = {1, 2, 3, 4, 5, 7}


 * Intersection (AND) **
 * The Intersection of two sets is A ** Ç ** B


 * It includes only those elements in __**both**__ A __**and**__ B


 * A ** Ç ** B = {1, 3}


 * Complement (NOT) **
 * The Complement of the set A is A'


 * It contains all elements that are __**not**__ in A


 * A' = {2, 4, 6, 8}


 * Example **


 * A sport day is being organised among 50 students.
 * 30 students wanted to play basketball(B),
 * 25 students wanted to play soccer (S)
 * and 5 didn't want to play either of these.
 * Draw a Venn Diagram of this situation
 * How many students wanted to play both basketball (B) and soccer (S)?


 * Solution **
 * students wanting to play = 50 – 5 = 45
 * B È S = 45
 * total of soccer plus basketball = 30 + 25 = 55
 * this is more than students wanting to play so some must be in both groups
 * Difference between total and students = 55 – 45 = 10
 * this means we must have counted 10 students twice, so 10 must be in the overlap
 * So 10 students wanted to play both
 * B Ç S = 10


 * **Note:** as a double check,
 * Inside the B (basketball) set is a total of 20 + 10 = 30
 * Inside the S (soccer) set is a total of 15 + 10 = 25
 * Including the 5 outside both circles, the total of students shown is 20 + 10 + 15 + 5 = 50
 * these numbers match the numbers given in the question so our diagram is correct.

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