(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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).

2. Relevant equations

N/A

3. 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!

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Elementary proof check/help

**Physics Forums | Science Articles, Homework Help, Discussion**