Do Functions Have Truth Values? I'm reading through a few analysis books and I am a little confused by some of the definitions that are given for functions. Some texts define functions to be some subset of the cartesian product of two sets, given that the elements of this subset satisfy the properties of a function. This is intuitively clear to me, but others first define the idea of a relation and then define functions to be a sort of relation that satisfies the typical properties of a function. 
This is confusing to me since I have always thought of relations as having truth values and functions as having no truth value. Is it appropriate to think of relations as having truth values and functions as not having truth values? Are the varying definitions compatible or is one wrong? I appreciate any help.

In logic we use predicate symbols to express that some relation holds between some number of objects .. and that would indeed be a claim with a truth-value. And we use function symbols to express functions that are used to map objects to other objects ... no claim or truth-value there.
But when we talk about a relation as a set of tuples, and a function as a specific kind of such a relation (one that is right-unique or 'functional'), we really don't make any claims in either case.
Example:
$1<2 $ is a claim involving a relation.
$1+2$ is an operation involving a function ... not a claim
$R_< = \{ (x,y) | x < y \} = \{ (0,1), (0,2), (1,2) , ... \}$ is a relation .. no claim here
$+$ is a function .. and can be expressed as $\{(x,y,z) | x + y = z \} = \{ (0,0,0), (1,2,3), ... \}$ .. again, no claim here
