Moderate# Cartesian Product: Definition and Properties, Example

ABSALG-4QLMVN

The Cartesian product of two sets $A$ and $B$, denoted $A\times B$, is the set of *ordered* pairs $(a,b)$, with $a\in A$ and $b\in B$. Therefore $|A\times B|=|A||B|$.

In set notation:

$A\times B=\{(a,b)\mid a\in A\;{\rm and}\;b\in B\}$

Let $A=\{3\}$, $B=\{3,5,7\}$, $C=\{2,3,4\}$, $D=\{2,4\}$

Which of the following is true?