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.

Solution:

We know that if n (A) = p and n (B) = q ,

then n (A x B) = pq

Therefore, n (A x A) = n (A) x n (A)

It is given that n (A x A) = 9

n (A) x n (A) = 9

Hence,

n (A) = 3

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

We know that A x 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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NCERT Solutions Class 11 Maths Chapter 2 Exercise 2.1 Question 10

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.

Summary:

The Cartesian product A × A has 9 elements among which are found (- 1, 0) and (0, 1) is given. We have found that remaining elements of set A´A are (- 1, - 1), (- 1, 1), (0, - 1), (0, 0), (1, - 1), (1, 0), and (1, 1)