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  • 1. Let A = {–1, 2, 3} and B = {1, 3}. Determine (i) A × B (ii) B × A (iii) B × B (iv) A × A

Let A = \left \{ -1,2,3\right \} and B = \left \{ 1,3\right \}. Determine

I) AXB  ii)BXA  iii) BXB  iv) AXA

Answers (1)

Given data: A = \left \{ -1,2,3\right \} and B = \left \{ 1,3\right \}.

Now, let’s solve the problems one by one-

i)A \times B = \left \{-1, 2, 3}{ \right \} X \left \{1, 3}{ \right \}= \left \{(-1, 1), (-1, 3), (2, 1), (2, 3), (3, 1), (3, 3) \right \}

ii)B \times A = \left \{1, 3}{ \right \} \times \left \{-1, 2, 3}{ \right \}= \left \{(1, -1), (3, -1), (1, 2), (3, 2), (1, 3), (3, 3)}{ \right \}

iii)B \times B = \left \{1, 3}{ \right \} \times \left \{1, 3}{ \right \} = \left \{(1, 1), (1, 3), (3, 1), (3, 3)}{ \right \}

iv)A \times A = \left \{-1, 2, 3}{ \right \} \times \left \{-1, 2, 3}{ \right \}= \left \{(-1, -1), (-1, 2), (-1, 3), (2,-1), (2, 2), (2, 3), (3, -1), (3, 2), (3, 3)}{ \right \}

 

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