My discrete book is defining a function, f, as a special type of relationship in which if both and , then (and a relation is defined as a set of ordered pairs).
So, is the empty set not a function because it doesn't have any ordered pairs, or is it a function because it does not violate the definition of a function?
For each of the following relations, please answer these questions:
(1) Is it a function? If not, explain why.
(2) If yes, what are it's domain and range?
(3) Is the function one-to-one? If not, explain why.
(4) If yes, what is the inverse function?
a,b,c,d,e,... I already did
(1) Yes (trivially), because there are no ordered pairs in , it does not violate the definition of function.
(2) dom = im =
(3) Yes (trivially), since the definition of one-to-one is not violated
Above is how I wrote up my homework (but it's not due until Thu.), but I'm not confident it's the right answer.