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.
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.
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)
Latest Govt Job & Exam Updates: