Translating sentences into propositional logic

Question

a) Alice is wise, if she is a doctor.

b) If Alice spoke to Bob, then Eve overheard her.

c) If Alice is wise, then she will be neither poor nor unhappy.

d) Exactly two of Alice, Bob and Carol will get here on time.

e) Alice will succeed if and only if she works hard, unless she is hit by a bus.

Answer 1

Abbreviate “will be on time” with ”wbot”

a) Isa(Alice, doctor) => isWise(Alice)

b) Spoketo(Alice,Bob) => Overheard(Eve,Alice)

c) IsWise(Alice) => ¬((WillBe(Alice,poor)∨(WillBe(Alice,unhappy))

d) ((wbot(Alice)∧wbot(Bob)∧¬wbot(Carol)) ∨

(wbot(Alice)∧wbot(Carol)∧¬wbot(Bob))∨

(wbot(Carol)∧wbot(Bob)∧¬wbot(Alice)))

* I find e) to be ambiguous, here is one translation:

e) (¬willbehitbybus(Alice))=>

(willSucceed(Alice)<=>worksHard(Alice))

 

I would not advise answering this question in an iPhone, as I did...