Given the following two sets A 1 2 3 and B a b c what are

Given the following two sets, A = {1, 2, 3} and B = {a, b, c}, what are the following Cartesian product sets:

A × B

B × A

Solution

Given : A = { 1,2,3}

B = { a,b,c}

The Cartesian product of sets A and B is the set of all possible ordered pairs whose first element is from set A and the second element is from set B.

AXB = { (1,a),(1,b) ,( 1,c) , ( 2,a) , ( 2,b) ,( 2,c) , ( 3,a) , ( 3,b) , ( 3,c) }

The Cartesian product of sets B and A is the set of all possible ordered pairs whose first element is from set B and the second element is from set A.

BXA = { ( a,1) , ( a,2) , ( a,3) , ( b,1) ,( b,2) ,( b,3) ,( c,1) , ( c,2) , ( c,3) }