Question

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 )

Answer 1

Answer:

b. $( N^c \cap D ) \cup ( N \cap D^c )$

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

= $N\cap D^c$

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

= Subscribe Daily informer and not subscribe News Magazine

= $D\cap N^c$

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

$= (N\cap D^c)\cup (D\cap N^c)$

$=( N^c \cap D ) \cup ( N \cap D^c )$