Homework 2

(A and B are propositions) is satisfiable.

(A and B are propositions) is unsatisfiable.

A, B are propositions, we have

These 4 sentences are all equivalent to each other

The expression: is in CNF form.

The clauses in the expression: are all in Horn form.

Sentence: entails Sunny

Sentence: is correct.

Choose all the correct options:

Consider the sentence in first order logic: HeightOf(X) (where X is a variable). Is the syntax of the expression correct in first order logic? Yes or No

Consider the sentence in first order logic: (where x,y are variables). Is the syntax of the expression correct in first order logic? Yes or No

The sentence in first order logic capture the English meaning: "Any small orange costs less than any large orange":

The sentence in first order logic capture the English meaning: "There is an animal that is cute and lazy":

The sentence in first order logic capture the English meaning: "All the pandas are cute and lazy":

The sentence in first order logic capture the English meaning:

"Every student in your school has a computer or has a friend who has a computer."

(The domain for both x and y consists of all students in your school.)

The sentence in first order logic capture the English meaning:

"There does not exist a woman who has taken a flight on every airline in the world."

where means “w has taken f”, and means “f is a flight on a.”. The domains of discourse for consist of all the women in the world, all airplane flights, and all airlines, respectively.

Use resolution to solve the following problem:

The knowledge base:

The query:

Does the knowledge base entail the query?