Foundation and Higher · Venn diagrams

Venn diagrams.
Start in the middle.

and, or, not:
three regions to know

two groups that can overlap —

Both

the overlap holds people in both sets

fill that in first

step 1 of 4

Fill it in

1. 30 students. 5 do both: that goes first.

2. French 12 − 5 = 7. German 15 − 5 = 10.

✓ Outside: 30 − 7 − 5 − 10 = 8

step 2 of 4

And: the overlap

1. French and German: the middle only.

2. 5 students out of 30.

✓ P(F and G) = 530 = 16

step 3 of 4

Or: inside either circle

1. French or German includes both.

2. 7 + 5 + 10 = 22 students.

✓ P(F or G) = 2230 = 1115

step 4 of 4

Not: outside that circle

1. Not French: outside the French circle.

2. 10 + 8 = 18 students.

✓ P(not F) = 1830 = 35

Venn diagrams —

Fill in

the overlap first, then subtract

And

the overlap only

Or

anything inside either circle

Higher notation: A ∩ B is “and”,
A ∪ B is “or”, A′ is “not A”.

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