empty set and intersection

**Jskid** · September 29th 2011, 10:03 PM

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

**emakarov** · September 30th 2011, 01:23 AM

Originally Posted by Jskid

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

It can be either depending on whether $\emptyset\in B$ .

**MoeBlee** · September 30th 2011, 07:58 AM

Originally Posted by Jskid

Why is $B \cap \{ \emptyset \} = \emptyset$ ?

$B \cap \{ \emptyset \} = \emptyset$ is NOT a theorem. Who said it is?

Originally Posted by Jskid

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

As emakarov alluded

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

**Jskid** · October 3rd 2011, 06:34 PM

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

**issacnewton** · October 3rd 2011, 09:25 PM

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

**MoeBlee** · October 4th 2011, 09:54 AM

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.

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