Venn Diagrams
🔒 Log in to trackChoosing the correct diagram
🔒 Log in to trackSome questions give three words and ask which picture shows them. Judge each pair of words on its own. The pair is nested, overlapping or separate. The correct picture agrees on every pair.
The three ways two words can relate
Take two words X and Y. Ask if every X is a Y, and if any X can be a Y.
| Relation | Test | Picture |
|---|---|---|
| Nested | Every X is a Y | X circle inside Y circle |
| Overlapping | Some X can be Y, not all | Two circles that cross |
| Separate | No X can be Y | Two circles apart |
Rule: Ask two questions. Is every X a Y? Can any X be a Y? The answers give the picture.
Nested words
A type sits inside its class. Every sparrow is a bird, and every bird is an animal.
So Sparrows, Birds and Animals make three circles, one inside the next. A part of a part is a part of the whole.
Tip: Go from the smallest word to the largest. Each word must fit inside the next.
Two types inside one class
Cats and dogs are both animals. But no cat is a dog.
So there is one big circle for Animals. Inside it are two separate small circles, Cats and Dogs. The small circles do not touch.
Words that cross
Some words share members but neither fits inside the other. Doctors, Women and Teachers are like this.
A woman can be a doctor. A doctor can be a teacher. But not every doctor is a woman. So each pair crosses, and you draw three crossing circles.
Watch: Do not put engineers inside females because you can think of women engineers. Male engineers also exist.
Mixed pictures
Some sets are a mix. Take Mothers, Females and Engineers.
Every mother is a female, so Mothers sit inside Females. Engineers can be female or male, and can be mothers or not. So Engineers cross both circles.
Common word sets
Exams repeat a few word sets. Learn the picture for each.
| Words | Picture |
|---|---|
| Surgeons, Doctors, Humans | Nested, one inside the next |
| Delhi, India, Asia | Nested, one inside the next |
| Pens, Pencils, Stationery | Two separate circles inside one big circle |
| Lawyers, Teachers, Women | Three crossing circles |
| Mothers, Females, Engineers | Mothers inside Females, Engineers crossing both |
| Pens, Books, Tables | Three separate circles |
Tip: Decide the picture for each set before you look at the options. Then match the option.
Question types you will see
Each type: how to recognise it, the method step by step, and one question to try.
Nested chain
Each word is a type of the next word: sparrow, bird, animal.
Check that every X is a Y.
Check that every Y is a Z.
Draw the circles one inside the next.
A part of a part is a part of the whole.
Which picture shows Sparrows, Birds, Animals?
Show solutionHide solution
Every sparrow is a bird.
Every bird is an animal.
Draw three circles, one inside the next.
Three circles, one inside the next
Two subsets in a bigger set
Two words are types of a third word, and the two are different from each other.
Find the widest word. Draw it as the big circle.
Check that the two other words cannot overlap.
Draw two separate circles inside the big one.
Both are inside the class, and no member is in both.
Which picture shows Cats, Dogs, Animals?
Show solutionHide solution
Animals is the widest word.
No cat is a dog.
Draw two separate circles inside one big circle.
Two separate circles inside a big circle
Partial overlaps
The words are jobs or traits that a person can have together, with none forced.
Ask if every X is a Y. If not, they are not nested.
Ask if some X can be a Y. If yes, they cross.
Do this for each pair.
If members can be shared but are not forced, the circles cross.
Which picture shows Doctors, Women, Teachers?
Show solutionHide solution
A doctor can be a woman, but not every doctor is.
A woman can be a teacher, but not every woman is.
A doctor can be a teacher, but not every doctor is.
Draw three crossing circles.
Three crossing circles
Mixed: inside and crossing
One pair is nested and a third word crosses the nested pair.
Find the pair with 'every X is a Y'. Nest it.
Test the third word against each of the two.
Draw it crossing the circles it overlaps.
Different pairs can have different relations in one picture.
Which picture shows Mothers, Females, Engineers?
Show solutionHide solution
Every mother is a female: Mothers inside Females.
Engineers can be female or male: they cross Females.
Engineers can be mothers or not: they cross Mothers.
Mothers inside Females, Engineers crossing both
Unrelated words
Three words have no link, such as objects of different kinds.
Ask if any member of one word can be in another.
If no, the circles are separate.
Draw three separate circles.
No shared member means no overlap.
Which picture shows Pens, Books, Tables?
Show solutionHide solution
No pen is a book.
No book is a table.
No pen is a table.
Draw three separate circles.
Three separate circles
Shortcuts that save time
Never judge the whole picture at once. Decide each pair, then pick the option that agrees with all three pairs.
Mothers, Females, Engineers. Which picture fits?
Show solutionHide solution
Mothers and Females: every mother is a female, so nested.
Engineers and Females: male engineers exist, women engineers exist, so crossing.
Pick the picture with a small circle inside Females and a crossing Engineers circle.
Mothers inside Females, Engineers crossing both
Find the widest word first. Draw it as the big circle. Then place the other words inside, across, or outside it.
Mistakes to avoid
Where most students lose marks on this subtopic.
Drawing engineers inside females because you thought of women engineers.
Male engineers exist too. So engineers cross females, and are not inside.
Making two types, like cats and dogs, overlap.
No cat is a dog. Draw two separate circles inside the class.
Judging the whole picture at once.
Check one pair at a time. Drop an option as soon as one pair is wrong.
Nesting words that only sometimes belong together.
Nest only when every X is a Y. Otherwise draw crossing circles.
Forgetting the class circle for two types.
Cats and dogs both sit inside animals. Draw the big circle.
Quick revision
Read this the night before the exam.
Ask: is every X a Y? Can some X be a Y?
Every X is a Y: X circle inside Y circle.
Some X can be Y, not all: crossing circles.
No X can be Y: separate circles.
Two types of one class: two separate circles inside the big circle.
Test pair by pair. One wrong pair removes the option.
Practice: 15 questions
Sets of 10, mixed across the question types above. Every answer has a step-by-step explanation.
Topic test · 10 questions
Suggested time 7 min · wrong answers go to your mistake notebook automatically.