Sets

• Sep 9th 2013, 12:43 AM
jcir2826
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?
• Sep 9th 2013, 02:48 AM
chiro
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.
• Sep 9th 2013, 08:17 AM
emakarov
Re: Sets
I will also denote the complement of X by X'.

Quote:

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.
• Sep 9th 2013, 08:25 AM
Plato
Re: Sets
Quote:

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 $A\cap B=\emptyset\text{ but }A'\cap B'\ne\emptyset.$
• Sep 9th 2013, 09:33 AM
HallsofIvy
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.