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

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$\Large\fbox{\color{purple}{QUESTION}}$

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.

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$\bf\Huge\red{\mid{\overline{\underline{ ANSWER }}}\mid }$

➡️We know that,

➡️If n(A) = p and n(B) = q, then n(A × B) = pq

➡️From the given,

➡️n(A × A) = 9

➡️n(A) × n(A) = 9,

➡️n(A) = 3 ……(i)

➡️The ordered pairs (-1, 0) and (0, 1) are two of the nine elements of A × A.

➡️Therefore, A × A = {(a, a) : a ∈ A}

➡️Hence, -1, 0, 1 are the elemets of A. …..(ii)

➡️From (i) and (ii),

➡️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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Answer 2

Answer:

➡We know that,

➡️If n(A) = p and n(B) = q, then n(A × B) = pq

➡️From the given,

➡️n(A × A) = 9

➡️n(A) × n(A) = 9,

➡️n(A) = 3 ……(i)

➡️The ordered pairs (-1, 0) and (0, 1) are two of the nine elements of A × A.

➡️Therefore, A × A = {(a, a) : a ∈ A}

➡️Hence, -1, 0, 1 are the elemets of A. …..(ii)

➡️From (i) and (ii),

➡️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).✔

Step-by-step explanation:

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