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Set language and notation
Set notation is a short way of describing groups of things. It links closely to Venn diagrams.
Key symbols
Sets are written in curly brackets.
Working with sets
ξ = {1, ..., 10}, A = {even numbers}, B = {multiples of 3}
A ∩ B = {6}
A ∪ B = {2, 3, 4, 6, 8, 9, 10}
A′ = {1, 3, 5, 7, 9}
A ∩ B = {6}
A ∪ B = {2, 3, 4, 6, 8, 9, 10}
A′ = {1, 3, 5, 7, 9}
Venn diagrams
Put the intersection in the overlap first, then the rest of each set, then everything else outside both circles.
ξ = {1, 2, ..., 12}, A = {factors of 12}. Find n(A′).
- A = {1, 2, 3, 4, 6, 12}, so n(A) = 6.
- n(A′) = 12 − 6 = 6
Answer: 6
∩ is AND (overlap). ∪ is OR (either). A′ is NOT A. n(A) counts elements. Fill a Venn diagram from the overlap outwards.
The interactive lesson includes the diagrams for this topic.
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