In his free time, Bob loves to charter a boat and sail the seven seas. In the following question, the domain is a set of the passengers on Bob's yacht. At sea, many passengers may feel seasick.

Therefore, define the following predicates:

P(x) : x drank purified water

D(x) : x took dramamine (motion-sickness medication)

M(x) : x still felt nauseous Translate each statement into a logical expression.

Then negate the expression by adding a negation operation to the beginning of the expression. Apply De Morgans law until each negation operation applies directly to a predicate and then translate the logical expression back into English.

Sample question: Some passenger drank purified water and took the medication.

1) x(P(x) D(x))

2) Negation: x(P(x) D(x))

3) Applying DeMorgans law: x(P(x) D(x))

4) English: Every passenger either did not drink purified water or did not take the medication (or both).

a) Every passenger did not take the medication.

b) Every passenger drank purified water or felt nauseous or both.

c) There is a passenger who did not take the medication and felt nauseous.

d) Every passenger who drank purified water felt nauseous. (Hint: Apply the conditional identity.)

e) There is a passenger who felt nauseous and drank purified water and took the medication.