# 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. Commented Aug 27, 2017 at 14:52
• take the book page as Universal set (ha ha) Commented Aug 27, 2017 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. Commented Aug 27, 2017 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. Commented Aug 28, 2017 at 4:41