Venn Diagram Practice — Two Sets

Practice bank for two-set Venn diagram questions in UCAT Decision Making.

---

Quick-Reference: Two-Set Venn Diagrams

The Inclusion-Exclusion Formula

$|A \cup B| = |A| + |B| - |A \cap B|$∣A∪B∣=∣A∣+∣B∣−∣A∩B∣

Where:

• $|A|$∣A∣ = total in set A (including overlap)
• $|B|$∣B∣ = total in set B (including overlap)
• $|A \cap B|$∣A∩B∣ = items in both A and B
• $|A \cup B|$∣A∪B∣ = items in at least one set

The Four Regions

Region	Formula
A only	$
B only	$
Both	$
Neither	$\text{Total} -

Step-by-Step Method

1. Start with the overlap (intersection) — this is the key value
2. Calculate "A only" = total A minus overlap
3. Calculate "B only" = total B minus overlap
4. Calculate "neither" = grand total minus sum of all three filled regions
5. Check: all four regions must add up to the grand total

Representing Logical Statements

Statement	Venn Diagram
All A are B	Circle A entirely inside circle B
No A are B	Circles do not overlap
Some A are B	Circles partially overlap

---

Strategy

• Always start from the intersection and work outwards
• Write numbers in each region as you go
• Final check: all regions must sum to the total
• Target: 45–60 seconds per question

---

Practice

Complete the 10 assessment questions. Each gives you set data and asks you to calculate a specific region or answer a question about the sets.