# Thread: empty set and intersection

1. ## empty set and intersection

Why is $\displaystyle B \cap \{ \emptyset \} = \emptyset$? Shouldn't it be $\displaystyle B \cap \{ \emptyset \} = \{\emptyset \}$?

2. ## Re: empty set and intersection

Originally Posted by Jskid
Why is $\displaystyle B \cap \{ \emptyset \} = \emptyset$? Shouldn't it be $\displaystyle B \cap \{ \emptyset \} = \{\emptyset \}$?
It can be either depending on whether $\displaystyle \emptyset\in B$.

3. ## Re: empty set and intersection

Originally Posted by Jskid
Why is $\displaystyle B \cap \{ \emptyset \} = \emptyset$?
$\displaystyle B \cap \{ \emptyset \} = \emptyset$ is NOT a theorem. Who said it is?

Originally Posted by Jskid
Shouldn't it be $\displaystyle B \cap \{ \emptyset \} = \{\emptyset \}$?
As emakarov alluded

$\displaystyle B \cap \{ \emptyset \} = \{\emptyset \}$ if and only if $\displaystyle \emptyset\in B$

4. ## Re: empty set and intersection

First page of section 2.2 in Discrete Mathematics for Logic and Foundations.

5. ## Re: empty set and intersection

are you sure about the name of the book. amazon doesn't come up with any book with that name

6. ## Re: empty set and intersection

Originally Posted by Jskid
First page of section 2.2 in Discrete Mathematics for Logic and Foundations.
Then, if you're quoting the book correctly, taking you to mean that the book claims it's a theorem of ordinary set theory, then the book is in clear error.