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Cartesian Product Of Sets


Ordered Pair : A pair of objects, listed in a specific order, is called an ordered pair, for example (a, b) is an ordered pair of two elements a and b, a is called the FIRST ELEMENT and b the SECOND ELEMENT.

Two ordered pairs (a, b) and (c, d) are equal if any only if a = c and b = d.

Cartesian product of Sets :
 Let A and B are two non-empty sets. The set of all ordered pairs (a, b) of elements a A and b B is called the Cartesian Product of sets A and B and is denoted by

A × B. Thus A × B = {(a, b) : a
A, b B}


Example : If A = {1, 2, 3} and B = {a, b}, then
(i) A × B = {(1, a)}, (1, b), (2, a), (2, b), (3, a), (3, b)}

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