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.
Relations and Functions || Class 11 CBSE || Maths
Relations and Functions || Class 11 CBSE || Maths
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Given that n(A * A) = 9
= > n(A) * n(A) = 9
= > p * p = 9
= > p^2 = 9
= > p = 3.
Clearly, Set A has 3 elements.
Since(-1,0) ∈ A * Aand (0,1) ∈ A * A.
= > (-1,0) ∈ A and 0 ∈ A
= > (0,1) ∈ A and 1 ∈ A
Therefore -1, 0, 1 ∈ A.
Hence A = {-1, 0, 1}.
Therefore remaining elements are :
{-1,-1}, { -1,1}, {0,-1}, {0,0}, {1,-1}, {1,0}, {1,1}.
Hope this helps!
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Heya !!!Since A × A = 9 elements
so , A would have 3 elements ( 3 × 3 = 9 )
Now , A × A contains ( -1 ,0 ) (0 , 1)
( -1 , 0 ) is in set A × A
So , -1 and 0 is in set A -------------(1)
Similarly
( 0 , 1 ) is in set A
so , 0 and 1 is in set A ------------(2)
From (1) and (2)
The 3 elements of A are -1 , 0 , 1
Hence A = ( -1 , 0 , 1 )
Now A × A = { -1 ,0, 1 } × { -1 , 0 , 1 }
A× A = { ( -1 × -1) , ( 0, 0 ) , ( -1 , -1 )
( 0 , -1 ) , ( 0 , 0 ) , ( 0 , 1 ) ( 1 ,-1 ) , ( 1 , 0 ) , ( 1 , 1 ) }
Remaining elements of A× A are ( -1 , 1 ) , ( -1 , 1 ) , ( 0, -1 ) , (0 ,0) , ( 1 , -1 ) , ( 1 , 0 ) and ( 1 , 1 )
hope it helps u dear ^_^