Phil 225 - Symbolic Logic
Homework 5
Due March 4, 2011

1) For each of the following sentences, assess whether it is valid in K. If it is, derive it from the axioms and rules of K. If it is not, give a K-model (specify the worlds, show which are related to which, and assign truth values to the sentential letters) in which it is false at some world. Be sure to specify which world in your model it is false in.

a)  (P  Q)  (P  Q)

b) (P ∨ Q   (P ∨ Q)

c) (P  Q)   (P ∧ Q)

2) For each of the following sentences, assess whether it is valid in S5. If it is, derive it from the axioms and rules of S5. If it is not, give an S5-model (specify the worlds and assign truth values to the sentential letters) in which it is false at some world. Be sure to specify which world in your model it is false in.

a) P  P (this one is hard)
b) P  P
c)  (P  P)
d)  (P  P)