WEEK 6 :: Homework

Construct countermodels demonstrating that the following arguments are invalid. (Work out the answers on paper first, and then input into ∃LOGIC v1 to check.)

C1. P ∴ Q

C2. (P→Q). Q ∴ P

C3. (P→Q) ∴ (Q→P)

C4. ((P∧Q)→R) ∴ (P→R)

C5. ((P→Q)∧R). (R∨P) ∴ Q

C6. (P→Q). (¬P→R). (¬Q→¬R) ∴ P

C7. (P→Q). (¬P→R). (¬Q→¬R) ∴ R

C8. (R↔S). (T→W). (¬S∨¬Q) ∴ (¬Q∨T)

C9. ¬(P∧¬Q). P ∴ P→(Q→¬P)

C10. ¬P→(Q∨R) . R→(Q→¬P). (Q→R) ∴ ¬(P↔Q)


Note that in ∃LOGIC, True is represented by lowercase "t" and False is represented by lowercase "f":

(And ignore the domain D for now.)