Let's say I have a subset of the Cartesian plane, for example:
$\{(x, y) \in R \times R: 2x+3 > 5\}$.
If I am asked to find the co-domain of the following set, how would I do so? I know how to find the domain, which is done by finding all possible $(x,y)$ ordered pairs and then placing all the $x$ values in a set. But how is this different from the co-domain?
Thank you very much!
On
To be clear, a set of ordered pairs in and of itself has neither a domain nor a codomain; domains and codomains are defined on functions.
If we assume the set of ordered pairs given by $\{ (x,y) \in \mathbb{R} \times \mathbb{R} : 2x+3>5 \}$ are all ordered pairs $(x,y)$ of some function $f:A \to B$ such that $x \in A$ and $y \in B$, then the domain $A$ consists of all $x \in \mathbb{R}$ such that $2x+3>5$, or in other words, $x>1$. And the codomain $B$ consists of all $y \in \mathbb{R}$ since there is no condition on $y$.
Normally, domain and co-domain are defined on functions, but we'll use your textbook's definition for domain and co-domain on relations.
In your relation, note that your set describes only the $x$-values, $2x+3>5$, i.e. $x>1$. So the $x$-values that satisfy this condition is your domain, as defined in your textbook. However, since there is no condition on your $y$-values, all of $\mathbb{R}$ is your co-domain.