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About LinkBacksCan anyone help with this
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.
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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