Question

Question #ea4c3

Answer 1

By writing out a few terms for the function z, we see that
`z={(1,1),(2,2),(3,8),(4,13),(5,8),(6,13),(7,8), 8,13),........}`

By definition, a function `f:X->Y` is onto (surjective) `iff AAy in Y, EE X in X` such that `f(x)=y`.

So in this case for example, `EE 4 in ZZ` such that `x(x) != 4 AA x in ZZ`.
`therefore z` is not onto.

By definition, a function `f:X->Y` is 1 -1 (injective) `iff f(x_1)=f(x_2)=>x_1=x_2`.

So in this case for example, `3!=5` but `z(3)=z(5)=8`.

`therefore z` is not 1 - 1.