Five classmates (Alicia, Beth, Carrie, Destiny, and Emily) are planning to be ro

Question

Five classmates (Alicia, Beth, Carrie, Destiny, and Emily) are planning to be roommates this semester to cut costs. However, while they’ve met before, they’re not all mutual friends on Facebook. The table below lists the Facebook friends in the group.

Let F(x, y) be the predicate “x is Facebook friends with y.” Translate each of the following predicates to English, and describe whether it is a true statement for these roommates.

(a) x, F(x, Alicia) ¬F(x, Emily)

(b) x, F(x, Carrie) F(x, Destiny)

(c) x, y, F(x, y)

(d) x, y, F(x, y)

Profile Facebook friends Alicia Carrie, Destiny, Emily Beth Emily Carrie Alicia, Emily Destiny Alicia, Emily Emily Alicia, Beth, Carrie, Destiny

Explanation / Answer

(a) x, F(x, Alicia) ¬F(x, Emily)
(b) x, F(x, Carrie) F(x, Destiny)
(c) x, y, F(x, y)
(d) x, y, F(x, y)

for some x ,x is facebook friend with Alicia and x is not friend with Emily
this is false as carrie is friend with Alicia and Emily both

for all x , x is friend with Carrie if and only if x is friend with Destiny
this is true as Carrie has friend Alicia and Emily and they are friend with Destiny too

for some x and all y x is friend of y
this is false as no person is friends with all

for all x and some y x is friend of y
this s true as all the persons are friends with some person atleast a single one

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