Cartesian product of a set with another cartesian product 
$A = \{a, b, c, d\}$
$C = \{ (1,2), (1,3), (2,4) \}$
$A \times C = ?$

Do I calculate this cartesian product like a regular cartesian product or are there any specific rules for calculating such an expression?
By the regular way, I mean like

$A \times C = \{(a, (1,2)), (a, (1,3)), (a, (2,4)), (b, (1,2)) ...\}$ and so on


You are right. However, the third element is $(a,(2,4))$ in your posting.
