Consider a small sorority. There are just four members - Abby, Bess, Cody, and Dana. Some of the girls like each other and some do not. Some are friends, and some are not. Some are younger than others. Your goal in this exercise is to encode examples of these relations in a way that satisfies various constraints on these relationships.

(1) The table on the left below illustrates one possibility for the "likes" relation, and the dataset on the right shows the corresponding information as sentential data. You can click on the squares in the table to check or uncheck those squares, and the dataset on the right changes accordingly. Your mission is to change the table on the left so that every girl likes herself and no one else. As you do so, note the changes to the dataset. This is a trivial exercise; it is intended mostly to illustrate the relationship between the representation of information in tabular form and in sentential form.

Abby Bess Cody Dana Abby       Bess       Cody   Dana

(2) Now, consider a variation of the Sorority World example in which we have a single binary relation, called friend. friend differs from likes in two ways. It is irreflexive, i.e. a person cannot be friends with herself; and it is symmetric, i.e. if one person is a friend of a second person, then the second person is friends with the first. Your mission here is to change the table on the left so that it satisfies the irreflexivity and symmetry of the friend relation and exactly six friend facts are true. Note that there are multiple ways in which this can be done.

Abby Bess Cody Dana Abby Bess       Cody       Dana

(3) Finally, consider a variation of the Sorority World in which we have a single binary relation, called younger. younger differs from likes in three ways. It is irreflexive, i.e. a person cannot be younger than herself. It is asymmetric, i.e. if one person is younger than a second person, then the second person is not younger than the first. It is transitive, i.e. if one person is younger than a second and the second is younger than a third, then the first is younger than the third. Your mission this time is to change the table on the left so that it satisfies the irreflexivity, asymmetry, and transitivity of the younger relation and so that the maximum number of younger facts are true. Note that there are multiple ways in which this can be done.