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Math Help - Express f as a subset

  1. #1
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    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) = {x + 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.
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  2. #2
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    Quote Originally Posted by GreenDay14 View Post
    I have a question here that asks:

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

    f(x) = {x + 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.
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