Question 1186889: Set C consists of the citizens of a certain town who voted "yes" for water
fluoridation. Set D consists of the citizens of the same town who have preschool
children. Define:
(a) C U D bar
(b) C bar (intersection) D
(c) C bar U D bar
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Let's define the sets and their combinations:
* C: Citizens who voted "yes" for water fluoridation.
* D: Citizens who have preschool children.
Now, let's define the requested set operations:
**(a) C ∪ D̄ (C union D complement)**
This represents the set of citizens who *either* voted "yes" for water fluoridation *or* do *not* have preschool children (or both). It includes everyone who voted yes, as well as all the citizens who do not have preschool children, even if they voted no.
**(b) C̄ ∩ D (C complement intersection D)**
This represents the set of citizens who *did not* vote "yes" for water fluoridation *and* *do* have preschool children. It's the group of parents of preschoolers who voted against fluoridation.
**(c) C̄ ∪ D̄ (C complement union D complement)**
This represents the set of citizens who *either* did *not* vote "yes" for water fluoridation *or* do *not* have preschool children (or both). It includes everyone who voted against fluoridation, and it also includes all the citizens who do not have preschool children, regardless of how they voted on fluoridation. This is equivalent to the complement of (C ∩ D).
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