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Set Theory

Set Theory Assignment / Homework Help

A set is a collection of clearly defined things, symbols or objects. Each object in a set is called an element of the set. A set should always be properly defined.

A set can be defined in two ways:
  • A set can be defined by listing all its elements for example,

    A = {1, 2, 5, 7, 8}
  • By describing the elements of the set for example,

    I = {x : x is an integer, x > 2}

We have to describe a particular property which all the elements x, in a set satisfy so that one can know whether a particular element belongs to the set.

An element of a set is denoted by symbol and denotes "is not an element of" or "does not belong to" for example,

If A= {2, 5, 7} then 2 A and 3 A


A set which does not contain any element is called a null set or empty set. It is denoted by the symbol Φ or { }.

Some examples of null set are: The set of triangles with 4 sides, the set of cars with 2 wheels, the set of cats with 6 legs etc.

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