1. ## Sets

Can anyone give me an example of two sets A and B such that A intersection B is empty but A complement intersection B complement is not?

2. ## Re: Sets

Hey jcir2826.

Let A and B = 0, A' and B = v. This means that (A and B) and (A' and B) = B = 0. So B is the empty set.

This means that for any A', A' and B = 0 since B is the empty set.

So its not possible to satisfy your condition.

3. ## Re: Sets

I will also denote the complement of X by X'.

Originally Posted by chiro
Let A and B = 0, A' and B = v. This means that (A and B) and (A' and B) = B = 0. So B is the empty set.
The OP needs A' ∩ B' ≠ ∅, not A' ∩ B ≠ ∅. Also, what is v and why is (A and B) and (A' and B) = B?

A' ∩ B' ≠ ∅ holds for most A and B, more precisely, unless A ∪ B is the whole universal set. So, you just need to find two small disjoint sets.

4. ## Re: Sets

Originally Posted by jcir2826
Can anyone give me an example of two sets A and B such that
A intersection B is empty but A complement intersection B complement is not?
.

Surely that says $A\cap B=\emptyset\text{ but }A'\cap B'\ne\emptyset.$

5. ## Re: Sets

Let U= {a, b, c, d}, A= {a}, B= {b}. then A complement is {b, c, d} and B complement is {a, c, d}. There intersection is {c, d}.

In fact, any example where $A\cup B$ is not the universal set will do.