Introduction to Logic

Exercise 1.5 - Logical Entailment

Consider the following premises about the state of Sorority World.

Dana likes Cody.
Abby does not like Dana.
Dana does not like Abby.
Bess likes Cody or Dana.
Abby likes everyone that Bess likes.
Cody likes everyone who likes her.
Nobody likes herself.

There are just four states of Sorority World that satisfy these sentences. They are shown below.

Figure 3 - Four states of Sorority World.

For each of the following sentences, say whether or not it is logically entailed by the premises shown above.

a. Abby likes Bess or Bess likes Abby.
b. Somebody likes herself.
c. Everybody likes somebody.