logics

1. Logics exercise - Must be pretty easy for mathematicians

Logics exercises (should be a cake walk for mathematicians) Hey, I was once challenged to find the answers to two exercises, on which I had success, but only by the means of trial and error. Could somebody show me the heuristics to solve them? The exercises are as follows: EXERCISE 1 There...
2. Another GCD Proof

Im new to the forum so im not sure if im posting in the right section but ive been stuck on this problem for days however im not sure on how to even go about it. I would at the very least need some advice on how to tackle this problem. (Headbang) Claim: For every pair of positive natural...
3. are there logics based on consistency "up to n proof steps"?

That is, in logic there are two basic ways of accepting a theory: (1) it is consistent (2) it is at least equi-consistent with some convenient theory, usually arithmetic However, the human brain only worries about consistency as far as one has time to think (having evolved a logic that was...
4. I need information related to four valued logics

To be more precise, I want to know wich are the four valued logics in use. I searched a lot but I'm not sure that I found allof them. They may be modeld by Boolean algebras, Heyting algebras, MV-algebras ( multi valued; like the Jan Łukasiewicz logic), etc. I'm interestited also in multi-valued...
5. Logics Help!!

I have a couple a problems I'm having a hard time defining ... Please Help!! 1. An enemy of Al is a friend of Bill. Therefore, anyone who knows the enemy of Al knows a friend of Bill. (Exy <-> x is an enemy of y; Fxy <-> is a friend of y; Kxy <-> knows y, a= Al, b= Bill) 2. Ptah is the...
6. Proposition Logics - Seriously need help!

Could anyone help me on this problem? i think i did it wrong it looks wierd so i was hoping if someone could show me where i went wrong. Prove the following using rules of inference. (p -> q) ^ (r -> s) ^ [t -> ~(q V s) ^ t => (~p ^ ~r) Set up P -> q ... H1(Hypothesis 1) r -> s ...
7. Can you prove that P, Q, or L [Propositional Logics]

I was given the following text: If Cleopatra was powerful, then she was venerated but if she was not powerful, then she was not venerated and she was feared. If Cleopatra was either venerated or feared, then she was a queen. Cleopatra was a leader if she was a queen. P = Cleopatra was...
8. Venn Diagram Logics

A garage that does state automobile inspections found that 12 cars failed because of bad tires, 23 cars failed because of bad brakes, 15 cars failed because of faulty exhaust systems, 9 cars failed because of bad tires and brakes, 8 cars failed because of bad brakes and exhaust systems, 5 cars...