I'm new to discrete maths and I have a few questions.
Let $C = \{x \in\mathbb{Z}: 0 < x < 10\}$ and let $D = \{ y \in\mathbb{Z}: 1 < y < 9\}$, and define a binary relation $S$ from $C$ to $D$ as follows:
For all $(x, y) \in C \times D$, $(x, y) \in S$ if and only if $y = 2x - 1$.
How to list down the ordered pair of $S$ if it has a range? What about the domain and range of $S$? Is it a function? How do I check?
The first thing to do is to write down all the elements of $S$. That is, to write down all the ordered pairs $(x,y)$ such that $x$ is in $C$ and $y$ is in $D$ and $y=2x-1$. Can you do that?
Then it's time to look up the definitions of "domain", "range", and "function", and check them against your list. Go try it, and come back if you get stuck.