Cartesian Product / Cross Product
The Cartesian product of n number of sets A1,A2,…An; denoted as
A1×A2⋯×An, can be defined as all possible ordered pairs
(x1,x2,…xn) where x1∈A1,x2∈A2,…xn∈An
Example: If we take two sets A={a,b} and B={1,2}
The Cartesian product of A and B is written as:
A×B={(a,1),(a,2),(b,1),(b,2)}
The Cartesian product of B and A is written as:
B×A={(1,a),(1,b),(2,a),(2,b)}
A subset R of the Cartesian product A × B is called a
relation from the set A to the set B. The elements
of R are ordered pairs, where the first element belongs to A and the
second to B.
For example, R
={(a,0),(a,1),(a,3),(b,1),(b,2),(c,0),(c,3)} is a relation from the
set {a,b,c} to the set {0,1,2,3}. A relation from a set A to itself
is called a relation on A.
practice questions here
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