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  • Help me understand! If set A={1,2,3} and set B={a,b}. Then cartesian prroduct AxB is?

If set A={1,2,3} and set B={a,b}. Then cartesian prroduct AxB is?

  • Option 1)

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

  • Option 2)

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

  • Option 3)

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

  • Option 4)

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

Answers (1)

best_answer

As we learnt

 

CARTESIAN PRODUCT -

A × B of two sets A and B is given by
A × B = {(a,b): a ∈ A,b ∈ B}

In particular R × R = {(x,y): x,y ∈ R} and R × R × R = (x,y,z): x,y,z ∈ R}
 

- wherein

If A= \left \{ 1,2 \right \}\: and\: B= \left \{ a,b \right \}

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

 

 The cartesian product is a set of ordered pairs of (a,b) where a\inA and b\inB.

 


Option 1)

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

Option 2)

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

Option 3)

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

Option 4)

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

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Himanshu

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