Introduction to Logic

Problem 7.1 - Boolean Models

Mr. Red, Mr. White, and Mr. Blue meet for lunch. Each is wearing a red shirt, a white shirt, or a blue shirt. No one is wearing more than one color, and no two are wearing the same color. Mr. Blue tells one of his companions, "Did you notice we are all wearing shirts with different color from our names?", and the other man, who is wearing a white shirt, says, "Wow, that's right!" Use the Boolean model technique and the following table to figure out who is wearing what color shirt. Clicking on an empty cell in the table makes that cell true; clicking on a true cell makes it false; and clicking on a false cell makes its truth value unknown.

  red white blue
Mr. Red      
Mr. White      
Mr. Blue      

The sentences in the table below capture the available information. As you change the world, the truth values of these sentences are recomputed and displayed in this table.

SentenceTruth Value
Each person is wearing a red shirt or a white shirt or a blue shirt. AX:EY:wears(X,Y)  
No one is wearing more than one color. AX:AY:AZ:(~wears(X,Y) | ~wears(X,Z) | same(Y,Z))  
No two people are wearing the same color. AX:AY:AZ:(~wears(X,Z) | ~wears(Y,Z) | same(X,Y))  
Each person's shirt color is different from the person's name. (wears(red,white)|wears(red,blue)) & (wears(white,red)|wears(white,blue)) & (wears(blue,red)|wears(blue,white))  
The man wearing the white shirt is not Mr. Blue. EX:(wears(X,white) & distinct(X,blue))