Monticello residents were surveyed concerning their preference for candidates Moore and Allen in an upcoming election. Of the 800 respondents, 300 support neither Moore nor Allen, 100 support both Moore and Allen, and 250 support only Moore. How many residents support Allen?
There are 800 residents.
300 support no one.
100 support both Moore and Allen.
250 support only Moore.
Therefore, the other 150 residents support someone, they don't support both, and don't support Moore, so they must support only Allen since there is no one else in the race.
We have to add the 100 residents who support both. 100 + 150 = 250.
This argument uses sets because we subtracted from the set of all residents the tree other sets to get the set of residents supporting Allen.