NCERT Class XI Mathematics - Relations and Functions - Solutions
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Question : 9
Total: 36
Let A and B be two sets such that n (A) = 3 and n(B) = 2. If (x, 1), (y, 2), (z, 1) are in A × B, find A and B, where x, y and z are distinct elements.
Solution:
Given, n(A) = 3 and n(B) = 2
Now (x, 1) ∈ A × B ⇒ x ∈ A and 1 ∈ B,
(y, 2) ∈ A × B ⇒ y ∈ A and 2 ∈ B
(z, 1) ∈ A × B ⇒ z ∈ A and 1 ∈ B
∴ x, y, z ∈ A and 1, 2 ∈ B
Hence, A = {x, y, z} and B = {1, 2}.
Now (x, 1) ∈ A × B ⇒ x ∈ A and 1 ∈ B,
(y, 2) ∈ A × B ⇒ y ∈ A and 2 ∈ B
(z, 1) ∈ A × B ⇒ z ∈ A and 1 ∈ B
∴ x, y, z ∈ A and 1, 2 ∈ B
Hence, A = {x, y, z} and B = {1, 2}.
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