If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that A x A = (B x

1.	If A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7}, Show that A x A = (B x B) ∩ (C x C).
Answer» A = {5, 6}, B = {4, 5, 6}, C = {5, 6, 7} A x A = {(5, 5), (5, 6), (6, 5), (6, 6)} … (1) B x B = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)} … (2) C x C = {(5, 5), (5, 6), (5, 7), (6, 5), (6, 6), (6, 7), (7, 5), (7, 6), (7, 7)} … (3) (B x B) ∩ (C x C) = {(5, 5), (5,6), (6, 5), (6,6)} … (4) (1) = (4) A x A = (B x B) ∩ (C x C) It is proved.

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

Answer»

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

A x A = {(5, 5), (5, 6), (6, 5), (6, 6)} … (1)

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

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

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

(1) = (4)

A x A = (B x B) ∩ (C x C)

It is proved.