Face-Off: Which Bono Venn Diagram Is Correct?

Have you seen the top Venn diagram on Facebook or Twitter based on the U2 song "With or Without You?"

I'm always pleased with math-type subjects creep their way into everyday life, and this diagram is no exception. (Little known fact to the general public: English and history teachers stole Venn Diagrams from mathematicians)

The top diagram is cute, and a good conversation-starter, but I don't know if it's correct.


Here's the lyrics in the chorus we need to dissect:

With or without you

With or without you

I can't live

With or without you

Quick background on Venn Diagrams:

• The Venn Diagram was published by John Venn in 1880. The intentional was to show relationship between elements (things) in any given comparison of sets (groups). (Source)
• The overlapping area of two or more sets is called the intersection. An intersection would be the subset of both overlapping sets.
• A set that describes everything that is in two or more sets is called the union
• In common language, an intersection is usually appropriate when "and" is the conjunction between two sets, and a union is appropriate when "or" is the conjunction.

It seems to me that the correct placement of Bono depends on where you're choosing to stress your interpretation. Is it in the double-negative spiral of "can't" and "without," or is it as cut and dry as "or and "and"?

Which diagram is correct? 

Further study on this topic:

"With or Without You Venn Diagram Meme"

"You, Bono, and a Venn Diagram"

"Bono Residency"