Counterexample for set identity

[WannabeNewton]

Homework Statement

Consider the function $$f:X \to Y$$. Suppose that A and B are subsets of X. Decide whether the following statements are necessarily true (I am including just the one I had trouble with):
(a) if $$A\cap B = \emptyset$$, then $$f[A]\cap f<b> = \emptyset </b>$$

Homework Equations

The Attempt at a Solution

I know this statement is false and I know I have to use a counter example. The problem is I am not at all good with counter examples. Could I use a discrete situation as a way of disproving the statement? For example, if I let $$X = \mathbb{R}$$, A = {-1, -2, -3}, B = {1, 2, 3}, and f = {(x,y): y = x^2} then $$A\cap B = \emptyset$$ but f[A] = f = {1, 4, 9} so $$f[a]\cap f<b>\neq \emptyset </b>$$. I don't know if this suffices as a counter example because it is a very specific example so I was hoping you guys could help me come up with one that would be credible?

 

[Dick]

There's nothing wrong with a counterexample being specific. That looks fine to me.

 

[WannabeNewton]

Oh ok. Thank you.

 

[micromass]

The LaTeX symbol for the emptyset is simply \emptyset

 

[WannabeNewton]

The LaTeX symbol for the emptyset is simply \emptyset

Fixed it thanks mate.