## WEEK 4 :: Homework

Construct L2 symbolisations for each of the following sentences.

S8. Loop and Lil are parakeets.

S9. Either Olivia studies or she doesn't pass.

S10. If the train is on time, then Olivia will make her flight and Frank won’t miss the show.

S11. Neither Mark nor Jen will finish their homework unless both work faster.

Using ∃LOGIC construct annotated derivations showing that the following arguments are valid.

1:34 W. ((P→W)→(R→T)) ∴ ¬T→(Q→¬R)

1:53 [T7] ∴ (((P→Q)→(P→R))→(P→(Q→R)))

2:3 (P↔¬Q)→R ∴ (¬R∧P)→Q

2:5 (S∨R)→Q. ¬(P∨¬S) ∴ ¬(P↔Q)

2:11 (P∨Q). ¬P. (T→P) ∴ (Q∧¬T)

2:15 (Q→P)→R. (¬Q∨S). ¬S ∴ (¬R→T)

2:17 (P∨R)→¬¬Q. (Q∧R)→P. R ∴ (P↔Q)

2:22 (R∨S). S→¬(Q→¬P) ∴ (P∨R)

http://www.elogic.brianrabern.net/