Question

The cartesian producy A * A has 9 elements among which are found (-1, 0) and (0, 1). Find the set A & the remaining elements of A * A ?

Give verified answer please otherwise i will reported ur answer.

Answer 1

Answer:

n(A×A)=9

Set A={−1,0,1} Since (−1,0) and (0,1)are elements in A×A

Remaining elements=

={(−1,−1),(−1,1),(0,−1),(0,0),(1,−1),(1,0),(1,1)}

Answer 2

Solution :

✎ We know that if n ( A ) = p and n ( B ) = q, then n ( A × B ) = PQ

∴ n ( A × A ) = n ( A ) × n ( A )

✎ It is given that n ( A × A ) = 9

⇒ n ( A ) × n ( A ) = 9

∴ n ( A ) = 3

✎ the order pairs ( -1 , 0 ) and ( 0 , 1 ) are two of the nine elements of A × A

✎ since n ( A ) = 3, it is clear that A = { -1, 0, 1 }

⇒ The remain elements of set A × A are ( -1 , -1 ), ( -1, 1 ) , ( -1 , 1 ), ( 0, -1 ), ( 0, 0 ), ( 1 , -1 ), ( 1 , 0 ) and ( 1 , 1 ).