9. Use De Morgan's Laws, and any other logical equivalence facts you

know to simplify the following statements. Show all your steps.

Your final statements should have negations only appear directly

next to the sentence variables or predicates (P, Q, E(x), etc.), and no

double negations. It would be a good idea to use only conjunctions,

disjunctions, and negations.

(a) ((-PAQ) V (R V ¬S)).

(b) ((P→ ¬Q) ^ (Q→ R)) (careful with the implications).

(c) For both parts above, verify your answers are correct using

truth tables. That is, use a truth table to check that the given

statement and your proposed simplification are actually logically

equivalent.