# Does a Venn diagram need a Universal set?

In my book there are questions where there are two intersecting sets $A$ and $B$ and the questions begin by saying something like "In the given Venn diagram ... ". But there is no Universal set surrounding the two sets $A$ and $B$. Just the two sets themselves. Strictly speaking is this kind of diagram an Euler diagram or a Venn diagram ? Does a Venn diagram need a Universal set ?

• There's an implied, unspecified universal set, but for all you know, it's just $A \cup B$. In any case, if you're not interested in points outside of $A \cup B$, there's no need to show an enclosing box. – quasi Aug 27 '17 at 14:52
• take the book page as Universal set (ha ha) – MAN-MADE Aug 27 '17 at 14:54
• It's implied if not present. A Venn diagram is more general than an Euler diagram because the presence of an overlap between set representations does not implies the existence of elements in that overlap. – Joffan Aug 27 '17 at 14:54
• As a somewhat different way of looking at it, some relations between sets (union, intersection, difference) do not require a universal set, while others (compliment) do. You can use Venn/Euler diagrams to represent the former, which doesn't require you to specify a universal set. – Kajelad Aug 28 '17 at 4:41  