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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.

Q10  The Cartesian product A \times A has 9 elements among which are found (–1, 0) and
         (0,1). Find the set A and the remaining elements of A \times A

Answers (1)
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It is given that Cartesian product A × A having 9 elements among which are found (–1, 0) and (0,1).
Now,
Number of elements in (A× B) = (Number of elements in set A) × (Number of elements in B)
n(A \times A) = n(A) \times n(A)
It is given that  n(A \times A) = 9
Therefore,
 n(A) \times n(A) = 9
\Rightarrow n(A) = 3
Now,
By definition A × A = {(a, a): a ? A}
Therefore,
-1, 0 and 1 are the elements of set A 
Now, because, n(A) = 3 therefore, A = {-1, 0, 1}
Therefore,
the remaining elements of set (A × A) are
(-1,-1), (-1,1), (0,0), (0, -1), (1,1), (1, -1) and (1, 0)

 

 

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