Solved mathematical logic problems to practice reasoning

 

(0) Mathematical logic problems : Solution 0.2

0.2 A journalist interviews a centenarian elderly man and he reveals the secret of his longevity, which according to him lies in his diet. The old man says:

"If I don't drink beer, then I eat fish" = ¬p -->q

"I don't eat fish if I have ice cream or don't drink beer" r ∨ ¬p -->¬q

Is it possible to follow such a regimen? What is the secret ingredient of his longevity?

      -1. ¬p-->q      
      -2. r ∨ ¬p -->¬q      
    3.1 p     3.2 q    
  4.11¬(r ∨ ¬p)   4.12 ¬q 4.13¬(r ∨ ¬p)   4.14 ¬q  
  5.11 ¬r   OPEN 5.13 ¬r   X  
  6.11 p     6.13 p      
               
               

 

Three alternatives in his diet:

 

1. Beer and no ice cream.

2. Beer and no fish.

3. Beer, fish, and no ice cream.

 

The ingredient for longevity is Beer! What a lover of hops!