Notation for list of list of pairs

Question

If i have ordered list (L) of pairs of two elements (one element from each set X & Y), how do represent such list? and if i have another list (T) which is list of L, what will be the notation of this? Also, what will the notation to say reject the list Li if last n elements (of type above pair) of list belongs to any list of T, what will be the notation of this?

Answer 1

I would represent $L$ as an ordered set of tupples, i.e. as $L=\{(x_i,y_i)\}_{i\in\{1,\ldots, N\}}$.

Now, I would somehow stop here with representing lists of lists of lists, and simply say something along the line of "Let $\Omega$ be the set of all such ordered sets of tupples, i.e. $\Omega=\{L|L=\{(x_i,y_i)\}_{i\in\{1\ldots N\}}\}$". Then go on by simply saying that $T\subset\Omega$. Finally, define the equivalence relation $\approx_N$ by saying that $L_1\approx_N L_2$ if the last $N$ elements of $L_1$ and $L_2$ are equal. Then you can simply say: I reject $Li$ if there exists an $L\in T$ with $Li\approx_N L$.