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What is the Cartesian product of $A=\{1,2\}$ and $B=\{a,b\}$?

  1. $\{(1,a),(1,b),(2,a),(b,b)\}$
  2. $\{(1,1),(2,2),(a,a),(b,b)\}$
  3. $\{(1,a),(2,a),(1,b),(2,b)\}$
  4. $\{(1,1),(a,a),(2,a),(1,b)\}$
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Option C
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Best answer
$A=\left\{1,2\right\}$

$B=\left\{a,b\right\}$

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

The above operation performed on sets $A$ and $B$ is called Cartesian Product, which is defined as:

$A\times B=\left\{(a,b)\mid a \in A \land b\in B\right\}$

Option $(C)$ is correct.
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