# Null set minus null set

1. Oct 3, 2012

### Aziza

What is ∅-∅ equal to?
Logically this is represented as the set containing all x such that x$\in$∅ and x$\notin$∅. I am confused on how to interpret this...I think the answer would just be the null set, but I am not sure. Could someone please clarify this?

2. Oct 3, 2012

### happysauce

Think of the subtraction of sets as the intersection of the one with the complement of the other. That is ∅$\cap$ ∅$^{c}$

3. Oct 3, 2012

### vela

Staff Emeritus
There is no $x$ for which $x \in \emptyset$ and $x \notin \emptyset$, so there are no elements in $\emptyset - \emptyset$.

4. Oct 3, 2012

### Staff: Mentor

Makes me think of the song quite a few years back, "Nothin' from nothin' leaves nothin." - Billy Preston, 1975

5. Oct 3, 2012

### SammyS

Staff Emeritus
Great post, Mark !

6. Oct 3, 2012

7. Oct 3, 2012

### Hurkyl

Staff Emeritus
That is exactly right. It may help to simplify that logical expression, because you can, for example, replace $x \in \emptyset$ with a truth value.

Or maybe slightly reorganizing it to the fact that

x is in ∅-∅​

is synonymous with

x$\in$∅ and x$\notin$∅​