Introduction to Logic

Exercise 1.1 - Evaluation

This problem 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

The sentences in the table below describe some relationships among the girls, with an indication of whether they are true or false in the world depicted in the first table. For each of the sentences, say whether it is true or false in the world pictured above.

Abby likes Dana.
Dana does not like Abby.
Abby likes Cody or Dana.
Abby likes someone who likes her.
Somebody likes everybody.