# Thread: Express f as a subset

1. ## Express f as a subset

I have a question here that asks:

Let S = {1, 2, 3, 4, 5} and define f : S --> Z by

f(x) = {x² + 1 if x is even
{2x - 5 if x is odd
(the 2 brackets are meant to be one big bracket)

Express f as a subset of S x Z. Is f one-to-one?

I am very unsure as to where to even start with this question, any help would be greatly appreciate. Thanks a lot.

2. Originally Posted by GreenDay14
I have a question here that asks:

Let S = {1, 2, 3, 4, 5} and define f : S --> Z by

f(x) = {x² + 1 if x is even
{2x - 5 if x is odd
(the 2 brackets are meant to be one big bracket)

Express f as a subset of S x Z. Is f one-to-one?

I am very unsure as to where to even start with this question, any help would be greatly appreciate. Thanks a lot.

I guess this is trivial
f = {(1,f(1)), (2,f(2)), ... .... .... , (5,f(5))}

Find f(1), f(2) etc based on the given definition.

Note that any function (or a binary mapping) from S->F is a subset of SxF.
Which makes sense as any mapping is a special kind of pairing where as SxF is a set of all possible pairs.