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1Family Relations2Venn Diagrams3Odd One Out4Combinations5Classification6Who Has What7Order the Steps

Concept 2 of 7

Venn Diagrams: 3-Set Classification

1

Today's big idea

Nest one circle inside another only when every single member belongs to both.

Sharing some members means the circles cross; it does not mean one sits inside.

2

How it works

👀 What's going on?

Three words arrive with no picture, and before you can answer anything you have to decide how their circles sit. Getting that shape right is most of the work.

💡 Here's the trick

Three diagram typesAnimalsCatsInsideevery X is YABOverlapsome X are YABSeparateno X is YAsk: Is every X also a Y?YES → nested · SOMETIMES → overlap · NEVER → separate

Look at the shapes above. Three arrangements cover almost every question: one circle wholly inside another, circles that cross, and circles that never touch at all. Choosing between them comes before any counting.

🪄 How to do it

  1. 1.Match your three words to one of the shapes above.
  2. 2.Ask of each pair whether every member of one is also in the other.
  3. 3.Draw whole containment only when the answer is every single one.

✍️ Try it

Arrange Animals, Dogs and Cats. Then arrange Humans, Doctors and Women.

Dogs and Cats are two separate circles, both inside Animals, since no dog is a cat. Humans is the , with Doctors and Women inside it and crossing each other.

⚠️ Watch out

You might be thinking any two groups that share members should be drawn one inside the other. Only nest them when every member belongs. Some doctors are women and some women are doctors, but neither group swallows the other, so they cross.

🌟 Why this matters

Sorting things into groups that overlap is what libraries, shops and biology all do, and the picture is the same every time.
Exam tip: Say the sentence "every A is a B" out loud; if it is false, the circles cross.

3

Watch me solve one

Quanta solves it

“Watch how I think through one of these — then you try.”

THE PROBLEM

“Which Venn best represents Mammals, Whales, Birds?”

  1. 1

    Whales vs Mammals

    Every whale is a mammal → Whales inside Mammals.

  2. 2

    Birds vs Mammals

    Birds are NOT mammals → Birds is a separate circle.

  3. 3

    Pick the diagram

    Whales inside Mammals, Birds separate.

  4. 4

    Answer ✓

    Whales inside Mammals, Birds separate

Now you try one — same steps, different story 👇

4

See it in action

⚡ Time to play!

If EVERY A is a B, draw A inside B. If only SOME overlap, use crossing circles.

VENN · ROUND 1 OF 3

Which diagram fits: Dogs, Cats, Animals?

5

Quick check

✅ VERIFICATION

In a club, 18 play chess, 12 play carrom and 5 play both. How many play at least one of the two?

⚡ Finish the activity above first to answer.

Keep going!

Up next: Odd One Out

Most share a property, and one breaks it.

Concept 3 of 7 →