Question

If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that A × A = (B × B) ∩ (C × C)

Answer 1

A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}

A × A = {(5, 5), (5, 6), (6, 5), (6, 6)} ……….. (1)

B × B = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} …(2)

C × C = {(5, 5), (5, 6), (5, 7), (6, 5), (6, 6), (6, 7), (7, 5), (7, 6), (7, 7)} …(3)

(B × B) ∩ (C × C) = {(5, 5), (5, 6), (6, 5), (6, 6)} …(4)

(1) = (4)

A × A = (B × B) ∩ (C × C)

It is proved.