Question

Explain Cartesian product with example.

Answer 1

Cartesian Product: The Cartesian product of two sets A and B, denoted A × B, is the set of all possible ordered pairs where the elements of A are first and the elements of B are second. Example: A × ∅ = ∅ since no ordered pairs can be formed when one of the sets is empty.

Answer 2

Firstly, what is ordered pair?

A pair of objects written in a particular order is called an ordered pair.

For Example, (1,3)=(1,3)

$\textbf{What is Cartesian Product of two sets ?}$

Cartesian product of two sets A and B is the set of all those ordered pairs whose first coordinate is an element of A and the second coordinate is an element of B.

It is denoted by A × B and is real as ' A cross B '.

For example, Let A ={1,2,3}, B={3,5}

Then, A × B = {1,2,3}×{3,5}

= {(1,3),(1,5),(2,3),(2,5),(3,3),(3,5)}