FIND CARTESIAN PRODUCT OF TWO GIVEN SETS

If A and B are two non-empty sets, then the set of all ordered pairs (a, b) such that a ∈ A, b ∈ B is called the Cartesian Product of A and B, and is denoted by A x B .

Thus, A x B = { (a,b) |a ∈ A,b ∈ B } 

A × B is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of A and the second coordinate is an element of B.

B × A is the set of all possible ordered pairs between the elements of A and B such that the first coordinate is an element of B and the second coordinate is an element of A.

If a = b, then (a, b) = (b, a).

The “Cartesian Product” is also referred as “Cross Product”.

Question 1 :

Let A = {1, 2, 3} and B = {x | x is a prime number less than 10}. Find A x B and B x A.

Solution :

A = {1, 2, 3}

B = {x | x is a prime number less than 10}. 

B  =  {2, 3, 5, 7}

A x B  =  {(1, 2) (1, 3) (1, 5) (1, 7)(2, 2) (2, 3) (2, 5) (2, 7)(3, 2) (3, 3) (3, 5) (3, 7)}

B x A  =  {(2, 1) (2, 2) (2, 3)(3, 1) (3, 2) (3, 3) (5, 1) (5, 2) (5, 3) (7, 1) (7, 2) (7, 3)}

Question 2 :

If B × A = {(−2, 3),(−2, 4),(0, 3),(0, 4),(3, 3),(3, 4)} find A and B.

Solution :

In the Cartesian product B x A, first terms are set of elements of B and the second terms are set of elements of A.

B = {-2, 0, 3} and A = {3, 4}

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