Venn diagrams and inclusion–exclusion — Maths Olympiad practice

How to solve it

Do not count twice — “the “both” group sits inside each circle, so take it away once”

1. n(A or B) = n(A) + n(B) − n(both) — otherwise the “both” group is counted twice.
2. Only A = n(A) − n(both).
3. Neither = total − n(A or B). Both = n(A) + n(B) − n(A or B).

Use it for: Survey, club, language and “how many like neither/both” questions in Class 6–10 papers and the sets chapter.

Worked example: In a class of 40 children, 25 like cricket, 18 like football and 8 like both. How many like neither? → 5

✏️ Practice

Work it out in your head or on paper, type the answer and press Check. Stuck? Press “Show me how”.

🏁 Topic 32 test

20 questions. Check each answer, then go to the next one. Get 16 or more right to pass.

🏅 Sign in with Google to earn the 🔵 Venn Wizard badge when you pass — and a certificate when you finish all 13 topics of Part 4 · Class 5–10 problem solving. You can still take the test without signing in.

🖨️ Venn Diagram Worksheet for Maths Olympiad

• Worksheet set 1 (PDF)
• Worksheet set 2 (PDF)
• Worksheet set 3 (PDF)