Thread: 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.

Can anyone help with this

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!

Ok great...I see that now, but what would the domain, range and image be? Thanks for the help