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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. [tex]( N^c \cap D ) \cup ( N \cap D^c )[/tex]

Step-by-step explanation:

Here,

N = { x ∈ U | x subscribes to News Magazine },

D = { x ∈ U | x subscribes to The Daily Informer },

Such that N∩D ≠ ∅,

Now, the number of the set of people surveyed who subscribe only News Magazine

= Subscribe News Magazine and not Daily Informer

= [tex]N\cap D^c[/tex]

Similarly, the number of the set of people surveyed who subscribe only Daily informer

= Subscribe Daily informer and not subscribe News Magazine

= [tex]D\cap N^c[/tex]

Hence,  the set of people surveyed who subscribe to exactly one of the two news sources given

= Subscribe News Magazine and not subscribe Daily Informer or subscribe Daily informer and not subscribe News Magazine

[tex]= (N\cap D^c)\cup (D\cap N^c)[/tex]

[tex]=( N^c \cap D ) \cup ( N \cap D^c )[/tex]

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