Suppose that $f: X \rightarrow Y$ is a one to one function and $A \subseteq X.$ $A, X, Y$, are all sets. 

I am trying to decipher if the following statements are true or false. If true I will need to prove it and if false I must give a counterexample.

1. Suppose that $f: X \rightarrow Y$ is a one to one function and $A \subseteq X$ then $f(X -A) \subseteq Y - f(A)$.
2. Suppose that $f: X \rightarrow Y$ is a one to one function and $A \subseteq X$ then $Y - f(A) \subseteq f(X-A)$.

Here is the example I came up with it $f: N \rightarrow N$ be the function given by $f(x)= x^2$. 
Let $X=[0,4] A=[1,3] Y=[0,16]$
then $f(A)=[1,9]$
so $Y- f(A)= [0,1] \cup [9,16] $ and $f(X-A)= [0,16]$

so 

1. $[0,16] \subseteq [0,1] \cup [9,16] $
2. $[0,1] \cup [9,16] \subseteq [0,16]$

So the first would be true and the second would be false? Am I on the right track?