Question

The Cartesian product A × A has 9 elements among which are found (–1, 0) and (0, 1). Find the set A and the remaining elements of A × A.

Answer 1

The elements in the Cartesian product of set A×A are 9.

Thus, the elements in set A should be 3.

The pairs ( −1,​​0 ) and ( 0,1 ) are from Cartesian product of A×A.

The pair ( −1,​​0 ) belongs to A×A, so the elements −1 and 0 should be in set A.(1)

The pair ( 0,​​ 1 ) belongs to A×A, so the elements 0 and 1 should be in set A.(2)

From equations (1) and (2), the elements −1, 0, 1 should be in set A.

A×A={ −1,0,1 }​ ×{ −1,0,1 } ={ ( −1,−1 ),( −1,0 ),( −1,1 ),( −1,−1 ),( 0,−1 ),( 0,0 ),( 0,1 ),( 1,−1 ),( 1,0 ),( 1,1 ) }

Thus, the remaining elements of set A×A are,

( −1,−1 ),( −1,1 ),( 0,−1 ),( 0,0 ),( 1,−1 ),( 1,0 ),( 1,1 ).