Introduction to Logic

Exercise 6.4 - Relational Evaluation

This exercise concerns the interpersonal relations of a small sorority. There are just four members - Abby, Bess, Cody, and Dana; and there is just one type of binary relationship - likes. The following table below shows who likes whom. A check in a box of the table indicates that the girl named at the beginning of the row likes the girl named at the head of the column; the absence of a check means that she does not.

  Abby Bess Cody Dana
Abby    
Bess    
Cody    
Dana    

The following sentences are constraints that characterize the possibilities. Your job here is to select a truth value for each constraint indicating whether that constraint is satisfied by the table shown above.

a. likes(dana,cody)
b. ¬likes(abby,dana)
c. likes(bess,cody) ∨ likes(bess,dana)
d. y.(likes(bess,y) => likes(abby,y))
e. y.(likes(y,cody) ⇒ likes(cody,y))
f. xlikes(x,x)