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## Homework Statement

For all sets A, B, and C, prove or provide a counterexample the following statements.

(A [itex]\setminus[/itex] B) [itex]\cap[/itex] (C [itex]\setminus[/itex] B) = A [itex]\setminus[/itex] (B [itex]\cup[/itex] C).

## Homework Equations

N/A

## The Attempt at a Solution

I went ahead and said it was false, and provided a counter example. I'm new to this and just wanna make sure my thought process was correct and the statement is indeed false.

Counterexample:

Let A = {1,2,3}, B = {2,3}, and C = {1,2}.

A [itex]\setminus[/itex] B = {1} and C [itex]\setminus[/itex] B = {1}. Then (A [itex]\setminus[/itex] B) [itex]\cap[/itex] (C [itex]\setminus[/itex] B) = {1}.

B [itex]\cup[/itex] C = {1,2,3}. Then A [itex]\setminus[/itex] (B [itex]\cup[/itex] C) = {0}. Since {1} ≠ {0}, the statement is false.

It's more the last part, i.e. "Then A [itex]\setminus[/itex] (B [itex]\cup[/itex] C) = {0}" I want to make sure is correct. Thanks for your help!