← General Intelligence & Reasoning

Venn Diagrams

Choosing the right diagram for a group of words — nested circles, overlapping circles or separate ones; the standard relationships and their pictures; reading a numbered Venn diagram and answering "how many belong to exactly one", "at least two" and "all three"; the two-set and three-set counting formulas; solving from the innermost region outwards; questions that give totals and ask for an unknown region — with fully worked examples.

📑 Contents (6 sections)

Last reviewed 22 Sept 2026 · 5 min read

Which picture fits the words

The first family of questions gives three or four words and asks which diagram represents them.

Relationship Picture
Family, Mother, Father one big circle containing two separate smaller ones
Vegetables, Potato, Onion same shape — two distinct kinds inside one class
India, Delhi, Mumbai one circle containing two separate ones
Men, Fathers, Doctors men containing fathers, doctors overlapping both (a doctor may be a woman)
Pen, Pencil, Stationery stationery containing two separate circles
Animals, Dogs, Cats animals containing two separate circles
Teachers, Women, Engineers three mutually overlapping circles
Sun, Moon, Star three separate circles (for this purpose)
Doctor, Surgeon, Human human ⊃ doctor ⊃ surgeon, fully nested
Exam TipAsk two questions about each pair

"Can something be both?" — if never, draw them apart; if always, nest them; if sometimes, overlap them. Do it for each of the three pairs and the diagram draws itself.

Reading a numbered diagram

A diagram of three overlapping circles has seven regions. Name them carefully:

  • Only A — inside A alone.
  • A and B but not C — the two-circle overlap, excluding the middle.
  • All three — the central region.
  • At least two — the three pairwise overlaps plus the centre.
  • Exactly two — the three pairwise overlaps without the centre.
  • Neither / none — outside all three circles.

Most marks lost here come from "at least two" being read as "exactly two".

The counting formulas

FormulaTwo and three sets

And with a universal set of people, those in none of the three .

Useful derived counts:

  • Exactly two
  • Exactly one

This chapter is in the syllabus of

Open an exam to see where this chapter sits in its syllabus, and to practise it.

✅ Free — no sign-up needed

How ready are you for General Intelligence & Reasoning?

Ten questions from the real syllabus, about five minutes. You will see your score and which subject is holding you back — before you create any account.

10 questions · no timer · no payment