Using predicate logic to solve text questions for 10-years-old?

63 Views Asked by At

I am going through a exam preparation book with a 10-years-old. I thought that predicate logic would make it easier to solve questions like the one below. My hope was to use Rules of Inference, but I struggle with it. I have not studied predicate logic explicitly and specifically have not studied translating English expressions. I am using the definitions of RFC2119 for MUST,SHOULD, etc. to help my understanding of the question.

With this background, my question is: Is there an easy way to translate the question below and prove that an answer is possible/impossible to construct with the given statements?

"

  1. If Emily does not have work, she is likely to have no money.
  2. If she has no money, she cannot afford her favourite car and will buy a cheaper car.
  3. If Emily has her favourite car, she will definitely drive to York."

If the above statements are correct, which one of the following could be true?

A) If Emily has work, she will definitely drive to York.

B) If Emily drove to York, she definitely has money.

C) If Emily does not have money, she might drive to York.

D) If Emily does not have work, she will definitely not drive to York.

The correct answer is given as B) in the preparation book.


My translation of the statements:

$1.) \neg Job => \neg Money$

$2.) \neg Money => \neg GoodCar$

$3.) GoodCar => GoToYork$

My translation of the answers:

$A.) Job => GoToYork$

$B.) GoToYork => Money$

$C.) \neg Money => GoToYork$

$D.) \neg Job => \neg GoToYork$


My idea was to list all expressions that we can generate through Modus Tollens (M.T.), which I understand as $ (p=>q) => ( \neg q => \neg p )$

$MT1.) Money => Job$

$MT2.) GoodCar => Money$

$MT3.) \neg GoToYork => \neg GoodCar $

Now we have 6 statements to check our answers against and I seem to come up with 'not enough information given' for all of the answers. Especially that there is no condition given under which a favourite car would be bought.