Thread: Deciding if a relation is a function

Hi everybody I'am going over some of the problems in my textbook preparing for my exam on monday and I have some doubts with the following problems:


"Decide whether each of the following relations is or is not a function and give the
type of those relations that are functions. Justify your answers.
a) R = {(a, b): a, b real and a + 3b2 = 1 }
b) R = {(a, b): a, b integers and floor(a + b) < ceil(b)}
c) R = { ((a, b), c) : a, b and c integers and a + b + c = 0}
d) R = {((a, b), c): a, b and c subset of a nonempty set A, and a U b = c} "

a and b i think I understand although I not 100% sure if I'm right but I think neither of them are functions.

c and d are giving me some trouble especially d, I think c is an algorithmic function b/c there is a unique solution for c which is -1*(a+b), for d i really have no clue any help will be appreciated thanks.

someone plz help??

c and d are functions.

Originally Posted by ps1313

Hi everybody I'am going over some of the problems in my textbook preparing for my exam on monday and I have some doubts with the following problems:


"Decide whether each of the following relations is or is not a function and give the
type of those relations that are functions. Justify your answers.
a) R = {(a, b): a, b real and a + 3b2 = 1 }
b) R = {(a, b): a, b integers and floor(a + b) < ceil(b)}
c) R = { ((a, b), c) : a, b and c integers and a + b + c = 0}
d) R = {((a, b), c): a, b and c subset of a nonempty set A, and a U b = c} "

a and b i think I understand although I not 100% sure if I'm right but I think neither of them are functions.

c and d are giving me some trouble especially d, I think c is an algorithmic function b/c there is a unique solution for c which is -1*(a+b), for d i really have no clue any help will be appreciated thanks.

What is your definition of "function"? That's where you should start. Specify how each of them does or does not satisfy the definition.