Sets arise in everyday life. E.g., a set of silverware, set of dishes, even a TV set. Why?
In everyday life a set is a group of objects belonging together in some way.
We can represent a set graphically as a circle or some other shape. This is called a Venn diagram. Any objects belonging to a set can be drawn as being inside the region. E.g., the vowels a, e, i, o, u belong to the set of vowels.
As you can see from the diagram, the vowels are contained within the alphabet.
We can use set-builder notation to designate the above set of vowels. V = {a, e, i, o u}. This read as the set of vowels, V, is composed of the elements a, e, i, o, and u.
Members of sets are called elements. So, for example, u is an
element of V. This can be written as u 
V. (u is an element of the set of vowels, V.)
Sets can be part of another set. E.g., the set of vowels is part of the set
of letters called the alphabet. Another way of saying this is, V is a subset
of the set of letters, A, the alphabet.
We can write this in math notation as V 
A. The set of
vowels is a subset of the alphabet.
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