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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. |
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Answer» 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 ordered pairs (–1, 0) and (0, 1) are two of the nine elements of A×A. We know that A × A = {(a, a): a ∈ A}. Therefore, –1, 0, and 1 are elements of A. Since n(A) = 3, it is clear that A = {–1, 0, 1}. The remaining elements of set A × A are (–1, –1), (–1, 1), (0, –1), (0, 0), (1, –1), (1, 0), and (1, 1). |
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