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

D Divya Saini

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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