Finding the possible positions of chess knight mathematically relative to a given position From this website I found the following question: 

A chess board’s 8 rows are labelled 1 to 8, and its 8 columns a to h. Each square of the board is described by the ordered pair (column letter, row number).
(a) A knight is positioned at (d, 3). Write down its possible positions after a single move of the knight.
(b) If R = {1, 2, ..., 8}, C = {a, b, ..., h}, and P = {coordinates of all squares on the chess board}, use set notation to express P in terms of R and C
(c) A rook is positioned at (g, 2). If T = {2} and G = {g}, express its possible positions after one move of the rook in terms of R, C, T and G.

For (a) is there anyway mathematically to list all the possible positions of the knight? I could for example, use a chess board to determine all the possible positions of the knight. 
About (C) I completely don't get it. 
The answers are provided in the website, however, I'm interested in how to solve them. 

For (a), you would move conveniently label the board position as $(4,3)$, and the $8$ possible destination squares as $(4\pm2,3\pm1)$ and $(4\pm1,3\pm2)$


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*Note, that's in answer to your question about listing the spaces mathematically. Using the original question notation, the knight's possible location after one move is $(\{c,e\},\{1,5\})\;\cup\;(\{b,f\},\{2,4\})$


Guessing at the unclear meaning of (c), I would say that the position of the rook after one move $(R,C)$ is: either $(R=G$ and $C \ne T)$ or  $(R\ne G$ and $C = T)$
Edit: And looking at the website you linked, I see that $R$ and $C$ are the set of possible values of rows and columns respectively, in which case I'd phrase my answer to (c) differently: the position of the rook after one move is defined by either $(R-G,T)$ or $(G, C-T)$
