Exercise 8.13 [language-determination-exercise]

Complete the following exercises about logical sentences:

1. Translate into good, natural English (no $x$s or $y$s!):

$${\forall\,x,y,l\;\;} SpeaksLanguage(x, l) \land SpeaksLanguage(y, l) \implies Understands(x, y) \land Understands(y,x).$$

1. Explain why this sentence is entailed by the sentence

$${\forall\,x,y,l\;\;} SpeaksLanguage(x, l) \land SpeaksLanguage(y, l) \implies Understands(x, y).$$

1. Translate into first-order logic the following sentences:

   1. Understanding leads to friendship.

   2. Friendship is transitive.

   Remember to define all predicates, functions, and constants you use.