The Cartesian product A × A has 9 elements ...

NCERT Class XI Mathematics - Relations and Functions - Solutions

Question : 10 of 36

Marks: +1, -0

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

= 9 ⇒ n(A) = 3

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).

Go to Question:

Prev Question

Next Question