The Survey Solver
Master practical Venn diagram problems with real-world surveys
📊 The Sorter (Interactive Survey)
A class of 30 students was surveyed. Adjust the sliders to see how the Venn diagram updates.
💡 The Intersection Rule: If you add n(Math) + n(English), you count the middle twice. So you must subtract n(Math ∩ English) to get the correct total.
📝 The Logic Track
💡 The Intersection Rule
When you add n(A) + n(B), you count the middle region twice. This is because people in the intersection belong to BOTH sets.
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
⚠️ EXAMINER TRAP
❌ WRONG: Adding all numbers without checking for double-counting.
✓ CORRECT: Always ask yourself: "Have I counted the middle twice?"
📊 FREQUENCY: Very Common
📉 MARK IMPACT: 2-3 marks
🎯 Algebra Strategy (Grade 9)
Step 1: Label the intersection as x
Step 2: Express all other regions in terms of x
Step 3: Sum all regions = Total
Step 4: Solve for x
📐 Notation Guide
n(A) = number of elements in set A
A ∪ B = union (elements in A OR B or BOTH)
A ∩ B = intersection (elements in BOTH A AND B)
A' = complement (elements NOT in A)
🧮 The Dynamic Solver (Venn Calculator)
Adjust the values below to see the step-by-step calculation.
✓ EXAMINER NOTE: In the exam, you MUST show each step clearly. Calculate "Only A", "Only B", and "Both" separately. Then add them for the union. This earns full method marks.
📋 Exam Technique Summary
✓ DO THIS:
- • Draw and label the Venn diagram first
- • Start from the middle (intersection)
- • Work outwards to "Only A" and "Only B"
- • Show all calculations clearly
- • Check: Does the total make sense?
❌ DON'T DO THIS:
- • Don't just add n(A) + n(B) without checking
- • Don't forget to subtract the intersection
- • Don't skip the "Only A" / "Only B" step
- • Don't write just the final answer
- • Don't confuse ∪ (union) with ∩ (intersection)
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