Cartesian product means a set consisting of all the ordered pairs (a, b) of two non empty sets A and B such that a ∈ A and b ∈ B. Cartesian product is denoted by A × B and defined as : A × B And defined as,
Symbolically:
A × B = { ( a, b) / a ∈ A and b ∈ B }
Cartesian product Example:
Let A = { 1, 4 } , B = { 3,4,6 }
then
A × B = { ( 1, 3) , (1,4 ) , ( 1,6) (4, 3) (4, 4) ( 4, 6) }
B × A = { (3,1) , (3 ,4 ) , ( 4 ,1) (4, 4) (6, 2) ( 6, 4) }
In general A × B ≠ B × A
Cartesian product of single set:
Let A = { 4, 8}
A × A = { 4, 8} × { 4, 8}
A × A = { ( 4 , 4) ,( 4 , 8) ,(8, 4) , ( 8, 8) }
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