Question

3. If \( B \times A=\{(-2,3),(-2,4),(0,3),(0,4),(3,3),(3,4)\} \) find \( A \) and \( B \). 4. If \( A=\{5,6\}, B=\{4,5,6\}, C=\{5,6,7\} \), Show that \( A \times A=(B \times B) \cap(C \times C) \).

Answer 1

We have A = {5, 6}, B = {4, 5, 6} and C = {5, 6, 7}

Now, A X A = {(5, 5), (5, 6), (6, 5), (6, 6)}

B X B = {(4, 4), (4, 5), (4, 6), (5, 4), (5, 5), (5, 6), (6, 4), (6, 5), (6, 6)}

And C X C = {(5, 5), (5, 6), (5, 7), (6, 5), (6, 6), (6, 7), (7, 5), (7, 6), (7, 7)}

Now, (B X B) ∩ (C X C) = {(5, 5), (5, 6), (6, 5), (6, 6)}

= A X A

Hence Proved