In set theory and logic, the overlapping circle diagrams used to represent relationships between sets are named after which mathematician?

Introduction / Context:
In mathematics and logic, diagrams made of overlapping circles are often used to visualise how sets intersect, combine or differ. These pictures help students understand union, intersection and complement of sets. They are named after the mathematician who popularised them. This question asks for that mathematician name.

Given Data / Assumptions:

• The context is set theory, logic and representation of sets.
• The diagrams consist of overlapping closed curves, usually circles.
• The standard name for these diagrams is well known in school mathematics.
• The options list several inventors and one mathematician.

Concept / Approach:
The familiar overlapping circle diagrams used to show set relations are called Venn diagrams. They are named after John Venn, an English logician and philosopher who used them to illustrate logical relations between classes. While other mathematicians such as Euler also used related diagrams, the standard term Venn diagram clearly points to John Venn.

Step-by-Step Solution:
Step 1: Recall that in textbooks, the diagram showing two or three overlapping circles to represent sets is called a Venn diagram. Step 2: Note that the surname in the term Venn diagram exactly matches John Venn. Step 3: Recognise that Lucien Vidi, Theophilus Van Kannel and Lewis Urry are linked to devices like early barographs, revolving doors and batteries, not to set theory. Step 4: Conclude that John Venn is the mathematician after whom these diagrams are named.

Verification / Alternative check:
Any basic set theory chapter or reasoning book refers to Venn diagrams by this name and usually includes a short note that they were introduced by John Venn. Although Euler diagrams existed earlier, the name Euler diagram is different. This clear naming correspondence between the diagram and the person confirms that John Venn is the correct choice.

Why Other Options Are Wrong:

• Lucien Vidi: Associated with improvements in barographs and pressure recording instruments, not set diagrams.
• Theophilus Van Kannel: Known for inventing the revolving door.
• Lewis Urry: Helped develop the modern alkaline battery.
• George Boole: A major figure in logic and Boolean algebra, but the overlapping circle diagrams are not named Boole diagrams.

Common Pitfalls:
Some learners may confuse the broader field of logic, where Boole played a major role, with the specific visual tool called a Venn diagram. They might think that since Boole worked on logic, the diagram must be linked to him. To avoid this, remember that Boolean algebra is a symbolic system, while the circular diagrams are specifically named after John Venn.

Final Answer:
The overlapping circle diagrams representing relationships between sets are named after the mathematician John Venn.