# Thread: Proof of Injective and Surjective

1. ## Proof of Injective and Surjective

Hey, i'm relatively new to the forums...just a little curious on how to solve this proof.

1. Determine whether f:Z X Z -> Z is onto if...
a) f(m , n) = 2m-n
c) f(m , n) = m+n+1
note: Z represents integers.

i) Determine if the function is Injective (one to one).
ii) Prove 1a.
iii) Determine if the function is Surjective (onto).
iv) Prove 1c.

3. Hey again!
It should be fixed now to the correct format.
According to the definition of Onto, "A function f: XY is surjective if and only if its range f(X) is equal to its codomain Y." So I'm guessing both a) and c) are onto because either way were going to end up with integers. Although, I'm not really sure how to prove this
.

4. For the first function.
Is this true $f(4,3) = f(5,5)$? So can the function injective?

If $z$ is an even integer then let $a=\frac{z}{2}\;\&\;b=0$. What is $f(a,b)$?

If $z$ is an odd integer then let $a=\frac{z + 1}{2}\;\&\;b=1$. What is $f(a,b)$?
Is $f$ onto (surjective)?

You do the second function.