1. CSC 8520 Spring 2010. Paula Matuszek
Puzzles from
SYMBOLIC LOGIC By Lewis Carroll
/files/28696/28696-h/
28696-h.htm
CSC 8520 Spring Paula Matuszek

2. CSC 8520 Spring 2010. Paula Matuszek
(1) Babies are illogical;(2) Nobody is despised who can manage a crocodile;(3) Illogical persons are despised.
What can we conclude from these statements?1. baby(X) ⇒ ¬(logical(X)) 2. manage(X) ⇒ ¬despised(X)
3. ¬(logical(X)) ⇒ despised(X) 1a. ¬(baby(X) ∨ ¬(logical(X))
2a. ¬manage(X) ∨ ¬despised(X)
3a. logical(X) ∨ despised(X)
(by way of ¬( ¬(logical(X))) ∨ despised(X) )
CSC 8520 Spring Paula Matuszek

3. CSC 8520 Spring 2010. Paula Matuszek
Resolve 1a and 3a:
¬baby(X) ∨ ¬logical(X)
logical(X) ∨ despised(X)
4. ¬baby(X) ∨ despised(X)
Resolve 4 and 2a.
¬baby(X) ∨ despised(X)
¬manage(X) ∨ ¬despised(X)
5. ¬baby(X) ∨ ¬manage(X)
CSC 8520 Spring Paula Matuszek

4. CSC 8520 Spring 2010. Paula Matuszek
Turning back into implication:
5. ¬baby(X) ∨ ¬manage(X)
becomes
baby(X) ⇒ ¬manage(X)
Or: babies can’t manage crocodiles!
Any other conclusions?
1a. ¬(baby(X) ∨ ¬(logical(X))
2a. ¬manage(X) ∨ ¬despised(X)
3a. logical(X) ∨ despised(X)
CSC 8520 Spring Paula Matuszek

5. CSC 8520 Spring 2010. Paula Matuszek
Any other conclusions?
1a. ¬(baby(X) ∨ ¬(logical(X))
2a. ¬manage(X) ∨ ¬despised(X)
3a. logical(X) ∨ despised(X)
CSC 8520 Spring Paula Matuszek

6. CSC 8520 Spring 2010. Paula Matuszek
Any other conclusions?
1a. ¬(baby(X) ∨ ¬(logical(X))
2a. ¬manage(X) ∨ ¬despised(X)
3a. logical(X) ∨ despised(X)
Resolve 2a and 3a:
6. ¬manage(X) ∨ logical(X)
People who can manage crocodiles are logical.
We also concluded (4) that babies are despised.
CSC 8520 Spring Paula Matuszek

7. CSC 8520 Spring 2010. Paula Matuszek
Try these:
10.
  (1) No one takes in the Times, unless he is well-educated;   (2) No hedge-hogs can read;   (3) Those who cannot read are not well- educated.
CSC 8520 Spring Paula Matuszek

8. CSC 8520 Spring 2010. Paula Matuszek
20.
(1) All members of the House of Commons have perfect self- command;   (2) No M.P., who wears a coronet, should ride in a donkey-race;   (3) All members of the House of Lords wear coronets.
CSC 8520 Spring Paula Matuszek

9. CSC 8520 Spring 2010. Paula Matuszek
30.
  (1) Things sold in the street are of no great value;   (2) Nothing but rubbish can be had for a song;   (3) Eggs of the Great Auk are very valuable;   (4) It is only what is sold in the street that is really rubbish.
CSC 8520 Spring Paula Matuszek

10. CSC 8520 Spring 2010. Paula Matuszek
40.
  (1) No kitten, that loves fish, is unteachable;   (2) No kitten without a tail will play with a gorilla;   (3) Kittens with whiskers always love fish;   (4) No teachable kitten has green eyes;   (5) No kittens have tails unless they have whiskers.
CSC 8520 Spring Paula Matuszek