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## Homework Statement

Consider the function [tex]f:X \to Y[/tex]. 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 [tex]A\cap B = \emptyset [/tex], then [tex]f[A]\cap f

**= \emptyset [/tex]**

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 [tex]X = \mathbb{R}[/tex], A = {-1, -2, -3}, B = {1, 2, 3}, and f = {(x,y): y = x^2} then [tex]A\cap B = \emptyset [/tex] but f[A] = f

## 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 [tex]X = \mathbb{R}[/tex], A = {-1, -2, -3}, B = {1, 2, 3}, and f = {(x,y): y = x^2} then [tex]A\cap B = \emptyset [/tex] but f[A] = f

**= {1, 4, 9} so [tex]f[a]\cap f****\neq \emptyset [/tex]. 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?**
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