TITLE: why is the intersection of two sets with no common element equal to the subset containing the empty set and not simply the empty set?
QUESTION [6 upvotes]: working through some notes and, in essence, the following is said: 
"$A=\{1,2\}$ and $B=\{3,4\}$
$A\cap B = \{\emptyset\}$"
Is this a mistake? Should it not be $\emptyset$?

REPLY [2 votes]: Hint,  The set $\{\emptyset \}$ has one element, but the set $\emptyset$ has no element.