CPSC 420 – Homework 1
due: Wednesday, March 21, 2007
1. Determine whether the following sets of propositional formulas are valid, satisfiable (but
not valid), or unsatisfiable by giving a truth table for each. Be sure to label each table with
your conclusion (valid, etc.), and indicate which truth assignments are satisfying.
a. {P→(Q→P)}
b. {(P→(Q→R)) →((P→Q)→(P→R))}
c. {(P∧(P→Q)) →Q}
d. {(P∧(P→Q)) → ¬Q}
e. {((M→X)∧ ¬X)→ ¬M}
f. {A→C, B →C, A ∨B , ¬C}
g. {P→Q, Q →R, P ∨Q, ¬Q∨ ¬R}
h. {(A⊕B⊕C),¬(A⊕B),¬(A⊕C),¬(B⊕C)}
2. Show that the proposition Ais entailed by the following set of sentences by deriving a
proof via Natural Deduction (i.e. using rules of inference). Recall that a proof (or derivation)
contains a sequence of sentences labelled with the indexes of the sentences they were derived
from, along with an indication of the inference rule used. (hint: think of various syntactic
transformations you can apply to the initial sentences.)
{D∧E→A, F ∧C→D, ¬(F∧C→B), C ∨B→E}
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