Question

2. The Cartesian product A×A has 9 elements among which (–1, 0) and ( , 0 1) are found.

Find the set A and the remaining elements of A×A.​

Answer 1

Given:

• n(A × A) = 9

• n(A) × n(A) = 9

• n(A) = 3

Solution

We know that,

• If n(A) = p

• n(B) = q

• n(A × B) = pq

• n(A × A) = n(A) × n(A)

We also Know that,

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

And, we know in A × A = {(a, a): a ∈ A}.

Thus,

–1, 0, and 1 has to be the elements of A.

• As n(A) = 3, clearly A = {–1, 0, 1}.

Hence,

The remaining elements of set A × A are as follows:

(–1, –1), (–1, 1), (0, –1), (0, 0), (1, –1), (1, 0), and (1, 1) .