iTechX

Question 1

?/? point (graded)

$(A \Leftrightarrow B) \land (\neg A \lor \neg B)$ (A and B are propositions) is satisfiable.

Question 2

?/? point (graded)

$\neg (A \lor B) \land \neg (A \Rightarrow B)$ (A and B are propositions) is unsatisfiable.

Question 3

?/? point (graded)

A, B are propositions, we have $\neg (A \land \neg B) \equiv \neg B \Rightarrow \neg A$

Question 4

?/? point (graded)

$((A \lor B) \land C) \equiv (A \lor C) \land (B \lor C)$

Question 5

?/? point (graded)

These 4 sentences are all equivalent to each other

Question 6

?/? point (graded)

The expression: $(A \lor B) \land C \land \neg D \land (E \lor F)$ is in CNF form.

Question 7

?/? point (graded)

The clauses in the expression: $(A \lor B) \land \neg C \land \neg D$ are all in Horn form.

Question 8

?/? point (graded)

Sentence: $Sunny \lor Monday$ entails Sunny

Question 9

?/? point (graded)

Choose all the correct options:

Question 10

?/? point (graded)

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

Question 11

?/? point (graded)

Consider the sentence in first order logic: $\forall x \forall y , Int(x) \land Int(y) \Rightarrow >(x,y)$ (where x,y are variables). Is the syntax of the expression correct in first order logic? Yes or No

Question 12

?/? point (graded)

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

$\forall x \forall y , [Orange(x) \land Small(x) \land Orange(y) \land Large(y)] \Rightarrow Cost(x) < Cost(y)$

Question 13

?/? point (graded)

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

$\exists x , Animal(x) \Rightarrow [Cute(x) \land Lazy(x)]$

Question 14

?/? point (graded)

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

$\forall x , Panda(x) \Rightarrow [Cute(x) \land Lazy(x)]$

Question 15

?/? point (graded)

The sentence in first order logic capture the English meaning: "No city in Jiangsu borders any city in Guangdong":

$\neg (\exists x,y,In(x, Jiangsu) \land In(y, Guangdong) \land Borders(x,y))$

Question 16

?/? point (graded)

The sentence in first order logic capture the English meaning: "No city in Jiangsu borders any city in Guangdong":

$\forall x, y, [In(x, Guangdong) \land In(y, Jiangsu)] \Rightarrow \neg Borders(x,y)$

Question 17

?/? point (graded)

The sentence in first order logic capture the English meaning: "No city in Jiangsu borders any city in Guangdong":

$\neg [\forall x \exists y ,In(x, Jiangsu) \land In(y, Guangdong) \Rightarrow Borders(x,y)]$

Question 18

?/? point (graded)

Use resolution to solve the following problem:

The knowledge base:

$B \land C \Rightarrow A$

$B$

$D \land E \Rightarrow C$

$E \lor F$

$D \land \neg F$

The query:

$A$

Does the knowledge base entail the query?

Homework 2