UPSC NDA Math Model Paper 7

Given: A = {1, 4}, B = {2, 3}, C = {3, 5}
Here, we have to find (A × B) ∩ (A × C)
As we know that, A × B = {(a, b) | a ∈ A and b ∈ B}
⇒ A × B = {(1, 2), (1, 3), (4, 2), (4, 3)}-----------(1)
⇒ A × C = {(1, 3), (1, 5), (4, 3), (4, 5)}-----------(2)
From (1) and (2) we can say that,
⇒ (A × B) ∩ (A × C) = {(1, 3), (4, 3)}
Hence, option A is the correct answer.