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Parin Sir > Quantitative Aptitude (Maths) > Set - Theory > OPERATIONS ON SETS > Cartesian  Product of  Two Sets > Cartesian  Product of  Two Sets

Cartesian  Product of  Two Sets

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☼ Cartesian  Product of  Two Sets  :   The Cartesian product  A \times B of  two non-empty sets  A  and  B  is defined as :  A \times B  =  { ( a, b ) :  a  \in A  and  b \in B }.

 (i) A \times B  = \emptyset    \large \Leftrightarrow  A  = \emptyset   or    B  = \emptyset  or   A  =  B  =  \emptyset

 (ii) In general,   A \times B  \ne  B \times A.

 (iii) n (A \times B)  =  n(A)  · n(B).

 (iv) If  either  A  or   B is an infinite set, then  A \times B  is an infinite set.

 

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