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).

$$ 2. Explain why this sentence is entailed by the sentence

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

$$ 3. 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.

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).

$$ 2. Explain why this sentence is entailed by the sentence

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

$$ 3. 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.

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).

$$
2. Explain why this sentence is entailed by the sentence

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

$$
3. 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.