# Thread: Questions on set theory

1. ## Questions on set theory

Hi

I need help with the following sets questions

Let A, B and C be sets. Prove that
i)$\displaystyle A\cap(B\setminus C)=(A\cap B)\setminus(A\cap C)$

Give an example of sets A, B and C for which
ii)$\displaystyle A\cup(B\setminus C)\neq(A\cup B)\setminus(A\cup C)$

I have other proofs of various sets but they involved truth tables. But since these sets involve a subtract set(\), i am not sure on what to do.

thanks

2. Hello,

Just recall that $\displaystyle A\setminus B=A\cap B^c$ (the complement of B) and use the usual properties of distribution and associativity of unions and intersections

3. For (ii)

Let $\displaystyle A\neq \emptyset$ and choose $\displaystyle B,C$ arbitrary.

4. Originally Posted by rpatel
Hi

I need help with the following sets questions

Let A, B and C be sets. Prove that
i)$\displaystyle A\cap(B\setminus C)=(A\cap B)\setminus(A\cap C)$
Agree with Moo
Give an example of sets A, B and C for which
ii)$\displaystyle A\cup(B\setminus C)\neq(A\cup B)\setminus(A\cup C)$

I have other proofs of various sets but they involved truth tables. But since these sets involve a subtract set(\), i am not sure on what to do.

thanks
Alternatively, Let $\displaystyle C=B=U$ where $\displaystyle U$ is the universal set. Then, $\displaystyle A\cup\left(U\cap U'\right)=A\cup\varnothing=A$ whereas $\displaystyle \left(A\cup U\right)-\left(A\cup U\right)=U-U=\varnothing$. I'm sure you can add the extra stipulation to finish this.