HW 5: Possible Answers

Even thought you were not allowed to, I have dropped outer parentheses, superscripts, and other parentheses that were not needed for unique readability.

(1)     Dab ® Icb

(2)     (–Dab ® Icb) , or (Dab Ú Icb)

(3)     –Dab ® -Icb  or Icb ® Dab

(4)     (Dab Ú –Dab) ® Icb  or
          (Dab ® Icb) Ù (–Dab ® Icb), or simply
          Icb

(5)     (Ld Ù Cd Ù Gd Ù –Dda) ® –Hba or
          (Ld Ù Cd Ù Gd) ® (–Dda ® –Hba)

(6)     Cb Ù (Jc « [Lc Ù –Icb]) [Note that the sentence entails that Barry is crazy, not that he is crazy if Cleo would be a good judge. Thus the clause 'Cb' must be outside the biconditional.. This was tricky.

2.

a)  Only the murderer (or the victim) could leave blood at a murder scene.

b)  Only those who were sick have a reason that would excuse late homework.

[This one is really tricky. I know it is tempting to say, "Being sick is the only reason for excusing late homework." This is close, but it’s not quite right. What you need is that if you weren’t sick then you have no reason to be excused. It is not necessary that in addition there be no other reason to be excused. For example spose you were sick but that your dog also died. The fact that being sick gives you a reason that would excuse your late homework doesn’t entail that the death of your dog can’t provide an additional reason that excuses you. In other words, only sick people can be excused -- but that doesn’t preclude the sick people from having other reasons beside being sick. Get it?

       c)  Being believed by me to be central to who I am is a property.

          d)  People never wait 10 years to talk about serious matters.

          e)  Thomas must have been either telling the truth or lying.