AIN-assignment

Convert the following formula into CNF (Conjunctive Normal Form):
¬(P→Q)

• P∧¬Q

• ¬P∨Q

• ¬P∧¬Q

• P∨¬Q

Which of the following is in CNF form?

•  (P∨¬Q) ∧ (R∨S)

• (P∧Q) ∨ (R∧S)

• (P→Q) ∧ (R∨S)

• ¬P ∨ (Q∧R)

Which of the following is the correct resolution rule for the clauses:
(P∨Q) AND (¬P∨R)?

• ¬Q∨R

• Q∧R

• P∨R

• Q∧¬R

What can be inferred using resolution?

• R∧S

• R∨S

• ¬R∧¬S

• P∧Q

If the following statements are true:

P→Q

Q→R

What can you conclude using transitivity?

• ¬P∨R

• P∧Q→R

• Q∨R

• P→R

Which of the following is logically equivalent to P ∨ (Q∧R)?

• (P∧R) ∨ (Q∧R) 

• (P∧Q) ∨ R

• (P∨Q) ∧ (P∨R)

• (P∨Q) ∧ R

Convert the following formula into CNF: (P→Q) ∧ (¬Q→R)

• (¬P∨Q) ∧ (Q∨R)

• (P∨¬Q) ∧ (R∨¬Q)

• (¬P∨Q) ∧ (¬Q∨R)

• (P∧Q) ∨ (R∧Q)

Which of the following is not in CNF form?

• (¬P∨Q) ∧ (R∨¬S)

• (P∧Q) ∨ (R∧S)

• (¬Q∨P) ∧ (S∨R)

• (¬P) ∧ (Q∨R)

Which of the following statements is unsatisfiable?

• (P∨¬Q) ∧ (Q∨R)

• (P∨Q) ∧ (¬P∨¬Q)

• (P∨Q) ∧ (¬P∨R)

• (P∧¬Q) ∨ (Q∧¬R)

Convert the following formula to CNF: ¬(P→Q) ∨ (R∧¬S)

• P ∧ ¬Q ∨ (R ∧¬S)

• (P ∧ R) ∨ (¬Q ∨¬S)

• (¬P ∨ Q) ∧ (R ∨ ¬S)

• (P ∨ ¬R) ∧ (Q ∨ S)