Venn Diagrams & Set Relationships in OC and Selective Thinking Skills
Learn how to solve Venn diagram and set relationship questions in NSW OC and Selective Thinking Skills, including all, some, none, only and must-be-true…
Venn Diagrams and Set Relationships in NSW OC and Selective Thinking Skills
Some Thinking Skills questions look complicated because they contain several statements about groups, such as:
all
some
none
only
not everyone
But underneath the wording, many of these questions are really testing one simple idea:
Which groups are inside other groups, which groups overlap, and which groups cannot overlap?
This is where a quick Venn diagram, or even a few simple arrows, can make the question much easier.
These relationships appear in both NSW OC Thinking Skills and NSW Selective Thinking Skills, often inside “must be true”, “whose reasoning is correct?” or logical deduction questions.
Students preparing for either test can practise these skills through NSW OC practice tests and NSW Selective practice tests.
1. “All A are B”
Suppose:
All violinists are members of the orchestra.
This means:
Violinist → Orchestra
Every violinist is in the orchestra.
But it does not mean every orchestra member is a violinist. They might play another instrument.
This is one of the most common reasoning traps in Thinking Skills: reversing a one-way relationship.
A useful rule is:
If A → B, you may move from A to B.
Do not automatically move from B to A.
2. Chaining relationships
Questions often combine several rules.
For example:
All falconers belong to the wildlife club.
Everyone in the wildlife club has completed safety training.
This gives:
Falconer → Wildlife Club → Safety Training
Therefore:
Falconer → Safety Training
Students do not always need to draw full circles. In a timed test, writing:
F → W → S
can be faster and clearer.
3. “No A are B”
Suppose:
No orchestra members are in the debating team.
The two groups cannot overlap.
If someone is in the orchestra, they cannot be in debating.
If someone is in debating, they cannot be in the orchestra.
This becomes especially useful when combined with another rule.
For example:
All violinists are orchestra members.
No orchestra members are debaters.
Therefore:
No violinists are debaters.
The answer may not be stated directly. Students often have to combine two conditions to reach it.
4. “Some A are B”
Suppose:
Some swimmers are runners.
This means at least one person belongs to both groups.
It does not mean:
all swimmers are runners
most swimmers are runners
most runners are swimmers
A useful habit is to mentally translate “some” as:
At least one.
This helps students avoid adding information that was never given.
5. “Not everyone”
This phrase is another common source of mistakes.
Suppose:
Not everyone in the art club plays an instrument.
This does not mean nobody in the art club plays an instrument.
It simply means:
At least one art-club member does not play an instrument.
There may still be many art-club members who do.
6. Be careful with “only”
“Only” can easily reverse the direction of a relationship.
Suppose:
Only members may use the private study room.
This means:
Uses study room → Member
If someone is using the room, they must be a member.
But being a member does not guarantee that they use the room.
A useful trick is:
When you see “Only A can B”, rewrite it as:
B → A
This makes the logical direction much clearer.
When should students draw a Venn diagram?
A Venn diagram is useful when several groups interact at once.
For example:
All basketball players enjoy running.
Everyone who enjoys running belongs to the fitness club.
No fitness-club member belongs to the chess club.
We can represent this as:
Basketball → Running → Fitness
and:
Fitness ✕ Chess
Therefore:
Basketball ✕ Chess
No basketball player can belong to the chess club.
The important skill is not drawing perfect circles. It is turning the language into a clear relationship.
Common traps
There are a few mistakes students should learn to recognise quickly.
Reversing the relationship
A → B does not automatically mean B → A.
Example:
All eagles are birds.
A bird is not necessarily an eagle.
Treating “some” as “most”
“Some musicians play tennis” could mean only one musician.
Do not assume anything about the majority.
Treating “not everyone” as “nobody”
These are very different.
Not every chef owns a restaurant.
means at least one chef does not own one.
It does not mean chefs cannot own restaurants.
Misreading “only”
Only students who submitted the form can attend.
means:
Attend → Submitted form
It does not mean:
Submitted form → Attend
Submitting the form may be necessary, but it may not be enough by itself.
Ignoring a chain
If:
A → B
B → C
then:
A → C
Students sometimes miss the answer because no single sentence states the final relationship.
“Must be true” versus “could be true”
This wording matters.
If the question asks:
Which statement must be true?
the correct answer must work in every possible situation that fits the rules.
A useful strategy is to try to break each option.
Ask:
Can I create a valid situation where this statement is false?
If yes, it is not something that “must” be true.
For “could be true”, the requirement is much weaker. Students only need to find one valid situation where the statement works.
A quick method for the test
Students can use this five-step process:
Identify the groups.
Translate each rule into arrows, overlaps or exclusions.
Combine the rules.
Check the direction carefully.
Test the answer options using only the information given.
For example:
“All S are R”
becomes:
S → R
“No R are C”
becomes:
R ✕ C
Therefore:
S ✕ C
This is often much faster than repeatedly rereading a long paragraph.
Why these questions matter
Venn diagram and set relationship questions are not really testing whether a child knows how to draw circles.
They test whether students can:
interpret precise language
distinguish what is stated from what is assumed
combine conditions
recognise one-way relationships
understand certainty versus possibility
make deductions from limited information
These same skills also appear in other Thinking Skills question types, including “Whose reasoning is correct?”, “Which statement must be true?” and reasoning mistake questions.
Once students become comfortable translating sentences into simple relationships such as:
A → B
A overlaps B
A ✕ B
many of these questions become much easier to manage.
At Selective Journey, students can practise Thinking Skills alongside Mathematical Reasoning, Reading and Writing.
For Selective High School preparation, explore the NSW Selective practice tests.
For Opportunity Class preparation, explore the NSW OC practice tests.
You can also register for a free trial.
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