Question

Let A = {1, 2} and B = {3, 4}. Write A × B. How many subsets will A × B have? List them.

Answer 1

The two sets are A and B.

A={ 1,2 }, B={ 3,4 }

The Cartesian product of two sets, A and B is,

A×B={ ( 1,3 ),( 1,4 ),( 2,3 ),( 2,4 ) }

The number of elements in the Cartesian product of A×B is 4.

Y= 2 n

Here, Y is the number of subsets in A×B.

Substitute the value n=4 in the above equation.

Y=16

Thus, the subset in A×B is 16.

Thus, the list of subsets is,

{ ( 1,3 ),( 1,4 ),( 2,3 ) ( 1,3 ),( 1,4 ),( 2,4 ) ( 1,3 ),( 2,3 ),( 2,4 ) ( 1,4 ),( 2,3 ),( 2,4 ) } ,{ ( 1,3 ),( 1,4 ),( 2,3 ),( 2,4 ) }

{ ( 1,3 ),( 1,4 ),( 2,3 ) ( 1,3 ),( 1,4 ),( 2,4 ) ( 1,3 ),( 2,3 ),( 2,4 ) ( 1,4 ),( 2,3 ),( 2,4 ) } ,{ ( 1,3 ),( 1,4 ),( 2,3 ),( 2,4 ) }