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. Prole Facebook friends Alicia Carrie, Destiny, Emily Beth Emily Carrie Alicia, Emily Destiny Alicia, Emily Emily Alicia, Beth, Carrie, Destiny 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) a) someone is facebook friends with Alicia and not with Emily b)everybody is facebook friends with carrie if and only if they are facebook friends with destiny. c)somebody is facebook friends with y d)everybody is facebook friends with y. these are my answers, but I am not too sure if they are correctly. can anybody help me out?

Explanation / Answer

a) For some x, x is facebook friend with Alicia and not with Emily

This is false, as the table shows that carrie is friends with both emily and Alicia.

b) For all x, x is friends with carrie if and only if x is friend with destiny.

This is true as carrie is friends with Alicia and emili and they are friends with destiny

c) For some x and all y , x is friends with y

This is flase as there is no one who is friends with all.

d) For all x and some y, x is friends with y

This is true as all the people have friends with some one

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