1. Which of the given formulas of PL is the best symbolization of the following sentence?
Pablo will go to the store if, and only if, his brother drives him and pays for gas.
2. Construct a complete truth table for the following argument. Then, using the truth table, determine whether the argument is valid or invalid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
M ∨ N
~M · O / N
3. Select the best English interpretation of the given arguments in predicate logic.
Wn ∨ Wm
(∀x)[Lx ⊃ (Dx ⊃ ~Wx)]
Ln • Dn	/ ~(∀x)~Wx
4. Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
H ≡ (I · ~J)
K ≡ ~H
~(K ⊃ J) / I ≡ J
5. Use indirect truth tables to determine whether each set of propositions is consistent. If the set is consistent, choose an option with a consistent valuation. (There may be other consistent valuations.)
(T ⊃ U) ⊃ (W ⊃ U)
T ⊃ ~(U ⊃ X)
(T ⊃ ~X) ⊃ W
