NCERT Class XI Mathematics - Relations and Functions - Solutions
© examsnet.com
Question : 10
Total: 36
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:
Since, we have n(A × A) = 9
⇒ n(A) × n(A) = 9 [Q n (A × B) = n(A) × n(B)] ⇒( n ( A ) ) 2
Also, given (–1, 0) ∈ A × A ⇒ – 1, 0 ∈ A and (0, 1) ∈ A × A ⇒ 0, 1 ∈ A
∴ –1, 0, 1 ∈ A
Hence, A = {–1, 0, 1} (Since n(A) = 3)
and the remaining elements of A × A are
(– 1, –1), (–1, 1), (0, –1), (0, 0), (1, –1), (1, 0), (1, 1).
⇒ n(A) × n(A) = 9 [Q n (A × B) = n(A) × n(B)] ⇒
Also, given (–1, 0) ∈ A × A ⇒ – 1, 0 ∈ A and (0, 1) ∈ A × A ⇒ 0, 1 ∈ A
∴ –1, 0, 1 ∈ A
Hence, A = {–1, 0, 1} (Since n(A) = 3)
and the remaining elements of A × A are
(– 1, –1), (–1, 1), (0, –1), (0, 0), (1, –1), (1, 0), (1, 1).
© examsnet.com
Go to Question: