A set is a collection, and the picture is two circles
Draw one circle for each set. Where the circles overlap are the things in both. The box around them holds everything you are choosing from, including whatever is in neither circle.
Class 11 · 12 games
Sets, explained with pictures
A set is just a collection of things, and you can ask what two of them share.
In everyday life: The students in your class who play cricket, and the ones who play chess. Some do both — those are the ones in the middle.
Union and intersection
The intersection A ∩ B is the overlap — the things in both. The union A ∪ B is everything in either circle, counted once. The word "or" in maths includes "both", so the middle belongs to the union too.
Adding the two totals counts the middle twice
If 13 play cricket and 10 play chess, that is 23 — but 4 people were counted in both totals. The real number of players is 23 − 4 = 19. That correction is the only formula in this topic: n(A ∪ B) = n(A) + n(B) − n(A ∩ B).
A worked example
In a class of 22, 13 play cricket and 10 play chess. 4 play both. How many play at least one?
19
Add the two totals and you get 23, but the 4 who play both have been counted twice — once in each total. Take those 4 off once: 13 + 10 − 4 = 19. The other 3 students play neither.
Words to know
- set
- A collection of things, with no repeats and no particular order.
- union (A ∪ B)
- Everything that is in A, or in B, or in both.
- intersection (A ∩ B)
- Only the things that are in both A and B.
- complement (A′)
- Everything in the box that is NOT in A.
In the games
You will read counts off a Venn diagram and work out what each set operation comes to.
Skills
- Sets, Venn diagrams and set operations · Class 11
By class
Class 11 sets (12)
Practise sets in Tivumo
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