Question

1. Find \( A \times B, A \times A \) and \( B \times A \) (i) \( A=\{2,-2,3\} \) and \( B=\{1,-4\} \) (ii) \( A=B=\{p, q\} \) (iii) \( A=\{m, n\} ; B=\phi \)

Answer 1

(i) We have

A = {2, -2, 3}, B = {1, -4}

A X B = {(2, 1), (2, -4), (-2, 1), (-2, -4), (3, 1), (3, -4)}

A X A = {(2, 2), (2, -2), (2, 3), (-2, 2), (-2, -2), (-2, 3), (3, 2), (3, -2), (3, 3)}

B X A = {(1, 2), (1, -2), (1, 3), (-4, 2), (-4, -2), (-4, 3)}

(ii) We have A = B = {p, q}

Then A X B = A X A = B X A  (\(\because\) A = B)

⇒ A X B = A X A = B X A = {(p, p), (p, q), (q, p), (q, q)}

(iii) We have A = {m , n}, B = ɸ

A X B = A X ɸ

A X B = {(m , m), (m, n), (n, m), (n, n)}

B X A = ɸ X {m, n} = ɸ

Answer 2

(i) We have A = {2, -2, 3}, B = {1, -4} A X B = {(2, 1), (2, -4), (-2, 1), (-2, -4), (3, 1), (3, -4)}

 A X A = {(2, 2), (2, -2), (2, 3), (-2, 2), (-2, -2), (-2, 3), (3, 2), (3, -2), (3, 3)} 

B X A = {(1, 2), (1, -2), (1, 3), (-4, 2), (-4, -2), (-4, 3)} 

(ii) We have A = B = {p, q}

 Then A X B = A X A = B X A  

( ∵ ∵  A = B) ⇒ A X  X A = B X A = {(p, p), (p, q), (q, p), (q, q)}

 (iii) We have A = {m , n}, B = ɸ A X B = A X ɸ A X B = {(m , m), (m, n), (n, m), (n, n)} B X A = ɸ

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