Questions on set theory

**rpatel** · January 16th 2010, 05:51 AM

Hi

I need help with the following sets questions

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

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

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

**Moo** · January 16th 2010, 06:00 AM

Hello,

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

**Dinkydoe** · January 16th 2010, 11:46 AM

For (ii)

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

**Drexel28** · January 16th 2010, 08:19 PM

Originally Posted by rpatel

Hi

I need help with the following sets questions

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

Agree with Moo

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

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

Thread: Questions on set theory

LinkBack

Thread Tools

Display

Questions on set theory

Similar Math Help Forum Discussions

Measure theory questions

Two set theory questions

Set theory questions

set theory questions

Theory questions

Search Tags