Here are some statements about puppies. Of course, you may not agree with all of them. But just suppose they were ALL correct, what conclusion could you draw from them?

(i) No puppy that chases cats is unteachable.

(ii) No puppy without a black nose will play with a Kangaroo.

(iii) Puppies with floppy ears always chase cats.

(iv) No teachable puppy has a loud bark.

(v) No puppies have black noses unless they have floppy ears.

Restating and re-ordering the statements using the standard conditional operator ( -> = if...then):

(3) Floppy ears -> Chases cats
(1) Chases cats -> Teachable
(4) Teachable -> Quiet Bark

(5) Floppy ears -> Black noses
(2) Plays with kangaroos -> Black noses

All of the possible conclusions:

A If a puppy has floppy ears it is teachable (3,1)
B If a puppy chases cats it has a quiet bark (1,4)
C If a puppy has floppy ears it has a quiet bark (3,1,4)

D If a puppy does not have a black nose, it does not have floppy ears, nor does it like to play with kangaroos. (5,2)

Posted by TomM on 2003-01-30 17:49:45