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At a family group meeting of 30 women, 17 are descended from George, 16 are descended from John, and 5 are not descended from George or John. How many of the 30 women are descended from both George and John?
in Set Theory & Algebra recategorized by
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Total Women = 30

Descended from John ($f(J)$) = $16$

Descended from George ($f(G)$) = $17$

Not descended from either John or George = $5$

$\therefore$ Descended from either John or George ($f(J) \cup f(G)$ = $25$

Women are descended from both George and John = $f(G) \cap f(J)$

$f(G) \cup f(J) = f(G) + f(J) – f(J)\cap f(g)$

$25 = 17 + 16 – f(J)\cap f(G)$

$f(J) \cap f(G) = 33-25 = 8$

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