Can anyone help with this

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- April 7th 2008, 08:24 PM #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.

- April 8th 2008, 05:52 PM #2

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- April 8th 2008, 06:10 PM #3
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!

- April 8th 2008, 08:22 PM #4

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