# Representing a logic puzzle with mathematical symbols

Consider the following logic puzzle, which is one of many created by Lewis Carroll, the author of Alice in Wonderland.

No birds, except ostriches, are 9 feet high.
There are no birds in this aviary that belong to anyone but me.
No ostrich lives on mince pies.
I have no birds less than 9 feet high.


Prove that these premises imply the following conclusion:

Any bird in this aviary does not live on mince pies.


Use the following symbols to represent statements:

H:  Height of the bird is not less than nine feet.
O:  The bird is an ostrich.
M:  The bird lives on mince pies.
I:  I own the bird.
A:  The bird is in this aviary.

1. Show the premises as logical formulas represented using these symbols. $$O \rightarrow H$$ $$A \rightarrow I$$ $$O \rightarrow \neg M$$ $$I \rightarrow H$$
2. Show the conclusion as a logical formula represented using these symbols. $$A \rightarrow \neg M$$
3. Show the negation of the conclusion using these symbols. $$\neg (A \rightarrow \neg M)$$
4. Show all premises and the negation of the conclusion as a set of clauses. $$A \wedge M, \neg O \vee H, \neg A \vee I, \neg O \vee \neg M, \neg I \vee H$$
5. Use the resolution method for your proof, and show for each resolution step which formulas are involved as parents and what the resolvent is. ???
• So where are you stuck? What have you done so far?? Or are you just asking someone else to do all your homework??? – Peter Smith Nov 5 '12 at 7:47
• Sorry, Peter. I added some of the things I had tried to do so far on the problem. I am very not sure if they are right. – entreband Nov 5 '12 at 10:30

Your formulation of the first hypothesis, "$O\to H$", says that an ostrich is necessarily at least 9 feet high. The first hypothesis as stated by Carroll, however, says that no other birds are that tall. If you formalize that information, I think you'll find the problem quite easy.