Three-set Venn diagrams and shading regions
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 1 real past-paper question with the answer explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- Three circles, eight regions
- Three sets, eight regions
- A filled diagram
- Filling three circles
Read the transcript of the teaching part
Last time
Before we start: last time, in Sets and Venn diagrams, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
Three circles, eight regions
Three overlapping circles make eight different regions. Cambridge gives you a set notation and asks you to shade exactly the right ones. Today you learn a calm, step by step way to shade any region. And to read a shaded region and name it in symbols.
Three sets, eight regions
With sets A, B and C there are seven regions inside the circles, and one outside. In the middle is the region in all three sets: A intersection B intersection C. Each pair of circles has an overlap that is in just those two sets, not the third. Then three petals that are in one set only, and the outside is in no set at all.
A filled diagram
Let the universal set be one to twelve. A is the even numbers, B is the multiples of three, and C is the factors of twelve. Six and twelve are in all three, so they go in the middle. Two and four are in A and C only. Three is in B and C only. Eight and ten are in A only, nine is in B only, one is in C only, and five, seven and eleven are outside. No number is in A and B but not C.
Filling three circles
Always start with the middle region, the elements in all three sets. Next fill each two-set overlap, taking away what is already in the middle. Then the single-set petals, and finally the outside. When you finish, add everything up. It must match the universal set.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Shading regions on a Venn diagram · Venn diagrams with three sets.
The whole chapter: Sets, Statistical Diagrams.
Chapter 2: Sets
- Set notation and two-set Venn diagrams 5 min
- Three-set Venn diagrams and shading regions 5 min
- Counting with a Venn diagram 5 min
Also for IGCSE Maths 0580
Which topics come up most in IGCSE Maths 0580 past papers, counted from every paper since 2004.