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Venn Diagrams and set notation

A Venn diagram is a graphical notation used to show membership of and relationships among set elements. Let us say for example that our universal set has numbers 1,2,3 and 4 such that:
Set A = {1,2}
Set B = {2,3}
Using ven diagrams, we can show the membership of elements in the universe as follows:

universal set elements

Union

A union of two sets is a collection of all elements in the set, ignoring duplicates. using a Venn diagram we can show the Union of sets A and B as follows:

This can also be written as A ∪ B = {1,2,3}

Intersection of sets

Intersection of two sets is the collection of elements that are in both sets. In other words, it is a collection of elements where the two sets overlap:

intersetion of two sets

Complement of a set

A complement of a set is a collection of all elements that are not in the set. In other words all elements in the universal set that are not in the set of interest. For example we can highlight A' as follows:

The difference of two sets

The difference of two sets is a collection of elements that are in one set that are not in the other. Thus A - B gives us:

Not in set notation

The NOT operator in set notation negates whatever the relationship is. For example, A intersection B can be shown as follows:

Notice how applying the not (~) operator changes the whole thing:

Not A intersection B

What sets succesful entrepreneurs apart?
Everyone aspires to the idea of owning and running their own business. Although the number of successful entrepreneurs has skyrocketed over the last few years, the number of failures has gone up by just as much if not more. It succeeding at business is not rocket s

Sets : Relationships
Equality - In the language of sets, two sets are equal if and only if all elements in set A are exactly the same as all elements of set B. Note that the order or arrangement and the number of occurrences for elements in a set does not matter. For example: A = { 1,2,3,4,5

Functions Notation

Set Notation
Set notation is a way of describing the membership of and relationships between groups of objects, called elements. The language also dictates that you have to have what is called the universal set which denotes ALL items under consideration. This is usually denoted by the symbol U.