Edit Problem


D unions intersections and complements
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Easy


In a group of $320$ people, only $10$ are millionaires but $4$ of the $170$ college graduates are millionaires. How many non-college graduates are not millionaires?

Answer:

$144$

Solution:

Let $\Omega$ denote the set of all $320$ people. Let $C$ and $M$denote the set of people that went to college and the set of millionaires,respectively. We have $|\Omega|=320$, $|C|=170$, $|M|=10$, and $|C\cap M|=4$.

We note that $M'\cap C'$ denotes the set of non-college graduates who are not millionaires.Now,\[\begin{align}|M'\cap C'|&=|(M\cup C)'|\\
&=|\Omega|-|(M\cup C)|\\
&=|\Omega|-(|M|+|C|-|M\cap C|)\\
&=320-(10+170-4)\\
&=320-176\\
&=144.\end{align}\]Therefore, $144$ non-college graduates are not millionaires.