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SET THEORY
SET:
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 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
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
NULL SET:
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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