We have A = {5, 6}, B = {4, 5, 6} and C = {5, 6, 7}
Now, A X A = {5, 6} X {5, 6}
= {(5, 5), (5, 6), (6, 5), (6, 6)}
And B X B = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}
Also C X C = {(5, 5), (5, 6), (5, 7), (6, 5), (6, 6), (6, 7), (7, 5), (7, 6), (7, 7)}
Therefore, (B X B) ∩ (C X C) = {(5, 5), (5, 6), (6, 5), (6, 6)}
= A X A
Hence Proved