The answer for part (a) is simple. For the part (b), the author states this answer
$$ S = \{(x,y) | 1 \leq x, y \leq 6 \} $$ But I feel this is incorrect. My answer is
$$ S = \{ (x,y) | 1 \leq x \leq 6, 1 \leq y \leq 6, x \in \mathbb{N}, y \in \mathbb{N} \} $$
What do you think?
Your answer is clearer. Alternatively, you could write
\begin{align} S&=\{(x,y)\in \mathbb{N}^2 \,|\, 1\leq x\leq 6, 1\leq y\leq 6\}.\\ \end{align}