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Math Help - one-to-one and onto

  1. #1
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    one-to-one and onto

    a) {(x,y): x,y e Z, x + y = 0}
    b) {(x,y): x,y e Z, xy = 0}
    c) {(x,y): x,y e Z, x^2 + y^2 = 1}

    For each of these, I have to answer:

    1) is this a function with range Z?
    2) If it is a function, what is its domain and image?
    3) If its a function, is it 1-1? onto? a bijection?
    4) If its a bijection, what is its inverse function?

    x,y e Z means x and y can be any integer (pos or neg). Sorry for the notation.

    Please Help! Thank you guys.
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  2. #2
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    Can anyone help with this
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  3. #3
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    If a relation is a function one requirement (not the only one) is that no two pairs can have the same first term.
    Both (0,1) & (0,2) are in the (b) relation. Can it be a function?
    Both (0,1) & (0,-1) are in the (c) relation. Can it be a function?

    You can prove that relation (a) is a function!
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  4. #4
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    Ok great...I see that now, but what would the domain, range and image be? Thanks for the help
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