Sets & Venn Diagrams
Union: A or B (everything in either set)
Intersection: A and B (only what's in both sets)
The formula:
|A union B| = |A| + |B| - |A intersect B|
Example: 30 students study French, 25 study Spanish, 10 study both.
Total studying at least one language = 30 + 25 - 10 = 45
Three-set problems:
|A union B union C| = |A| + |B| + |C| - |AB| - |AC| - |BC| + |ABC|
Neither: Total - |A union B| = those in neither set.
If there are 60 students total and 45 study a language, then 15 study neither.
GRE tip: Draw the Venn diagram. Fill in from the center (intersection) outward. The overlapping regions are where mistakes happen.
Reference:
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