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Let U represent the set of people in a certain community who were asked if they subscribe to an information source.
Let D ={ x ∈ U | x subscribes to The Daily Informer }
and
N ={ x ∈ U | x subscribes to News Magazine }


(Assume these sets are not disjoint.) Write the set that represents the set of people surveyed who subscribe to exactly one of the two news sources given.

a) N ∪ D
b) ( N c ∩ D ) ∪ ( N ∩ D c )
c) N c ∩ D
d) ( N ∩ D )c
e) ( N c ∪ D ) ∩ ( N ∪ D c )

Respuesta :

Answer:

b) ( N c ∩ D ) ∪ ( N ∩ D c )

Step-by-step explanation:

Let's see each option:

a) N ∪ D

This includes those who likes both, so this is not correc.t

b) ( N c ∩ D ) ∪ ( N ∩ D c )

Nc is the complement of N. That is those who do not subscribe to news magazine. Intensected with D, those are who do not subscribe to the news magazine but do to the daily informer. By the same logic, the second intersection are those who do subscribe to news magazine but not to the daily informer. This is the correct answer

c) N c ∩ D

This includes only those who subscribe to the daily informer but not to the news maganize. It also needs those who subscribe to the news magazine but not to the daily informer.

d) ( N ∩ D )c

This also involves those who do not subscribe to any of these news sources.

e) ( N c ∪ D ) ∩ ( N ∪ D c )

Wrong... Intersection of those who subscribe to the daily informer but not the news magazine and those who subscribe to the news magazine but not to the daily informer. This is the empty set.

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