Part A: Is the following a propositional expression/formula? If it is ambiguous say so!
~ stands for not
1) p
2) p /\ q /\ r
3) (p => q) \/ (q => +)
4) (p q)
5) (/\ p)
6) ~q
7) ~q /\ p
8) (~q) /\ p
9) (p <=> q) /\ ((~P) /\ (r \/ q))
10) => p
11) T \/ F
12) F => q
13) (F \/ q) /\ (T \/ p)
14) T ~


Part B: For each valid propositional expression above, compute the value using the
standard truth tables shown in class. Assume the following assignment:
A(p) = True
A(q) = False
A(r) = False

Assume the following precedence, ~ > /\ > \/ > => > <=>, which means we can drop some of
the parentheses without ambiguity.

Truth table for <=> is:
p   q   p <=> q
T   T     T
T   F     F
F   T     F
F   F     T


Part C: Construct truth tables for the following formulas:
1) (~p => (r => q)) /\ (q \/ p)
2) (p /\ r) \/ (q => r) /\ (p => r) <=> (p \/ r) /\ (q => r)


Part D: Characterize the following formulas as either satisfiable, falsifiable, unsatisfiable, unfalsifiable,
provide proofs of your characterizations, using a truth table(for unfalsifiable and unsatisfiable), or by
exhibiting assignments that show satisfiability or falsifiability:
1) (p /\ ~q /\ r) \/ (p /\ q /\ r) <=> (p /\ r)
2) (p /\ q) => ~p


Part E: Are the following formulas equivalent? Use the technique used in class to answer this question!
i.e is the LHS formula =? to the RHS formula(propositional expression)
1) ~p /\ q    =?      q => p
2) p /\ (q /\ r) =? (p /\ q) /\ r
3) ~(p /\ q)   =?  ~p \/ ~q
4) (p => q) /\ (~p => q)  =? q
5) p \/ (q /\ r) =? (p \/ q) /\ (q \/ r)
6) p => q  =? q => p
7) (p => q) /\ (q => p)  =? p <=> q
8) p => F  =? ~p