I am trying to formulate in a document some work done. However I have a problem defining the following. If I have a problem defined as the tuple $\langle X,Y \rangle$ such that $(x,(y_{11},y_{12},y_{13},\ldots,y_{1N}))$. How can I define this relation in cartesian products?
For example if X = {$x_{1},x_{2},x_{3}$} and N = 2 then Y = {{$y_{11},y_{12}$}, {$y_{21},y_{22}$}, {$y_{31},y_{32}$}} and should define the pairs ($x_{1}$, ($y_{11},y_{12}$)), ($x_{2}$, ($y_{21},y_{22}$)), ($x_{3}$, ($y_{31},y_{32}$)).
Thank you