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If A = \left \{ 1,2,3 \right \}, B = \left \{ a, b \right \} then A \times B is given by 

  • Option 1)

    \left \{ \left ( 1,a \right ), \left ( 2, b \right )\left, ( 3,b \right ) \right \}

  • Option 2)

    \left \{ \left ( 1, b \right ), \left (2,a \right )\right \}

  • Option 3)

    mmmm

    \left \{ \left ( 1,a \right ), \left ( 1,b \right ), \left ( 2,a \right ), \left ( 2,b \right ), \left ( 3,a \right ), \left ( 3,b \right )\right \}

  • Option 4)

    \left \{ \left ( 1,a \right ), \left ( 2,a \right ),\left ( 2,b \right ),\left ( 3,b \right )\right \}

 

Answers (1)

best_answer

As we learnt in 

Theorem of Cartesian Product -

(AXB)\cap (CXD)=(A\cap C)X(B\cap D)

-

 

 In castesian product, elements of A are paired with elements of B.

Thus,  A\times B=\left \{ (1,a),(1,b),(2,a),(2,b),(3,a),(3,b), \right \}


Option 1)

\left \{ \left ( 1,a \right ), \left ( 2, b \right )\left, ( 3,b \right ) \right \}

Incorrect

Option 2)

\left \{ \left ( 1, b \right ), \left (2,a \right )\right \}

Incorrect

Option 3)

mmmm

\left \{ \left ( 1,a \right ), \left ( 1,b \right ), \left ( 2,a \right ), \left ( 2,b \right ), \left ( 3,a \right ), \left ( 3,b \right )\right \}

Correct

Option 4)

\left \{ \left ( 1,a \right ), \left ( 2,a \right ),\left ( 2,b \right ),\left ( 3,b \right )\right \}

Incorrect

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