# I need help with this propositional logic problem

I study compound statements, and I encountered this problem in the book: The problem

I tried a solution: Let p be proposition "The first door leads to freedom" and let q be proposition "The warrior tells the truth". The question I am going to ask should help me to understand which door to choose. I can choose the correct door by knowing the value of p. So, I want to ask a question which results in yes (T) when p is true, and in no (F) when p is false regardless of which warrior am I asking. I built this truth table to understand what the question should be: My table

Then I tried to construct a compound statement with p and q according to my truth table. But then I realized that it has the same truth table as p, i.e. equivalent to it. I know that it's wrong because if I ask a such question, it is same as asking the warrior "Does the first door lead to freedom?", and obviously he can lie or tell the truth, so it doesn't help me.

The book provides a solution, but I can not understand it: Book solution

I do not understand what do columns "Desired Answer" and "Truth table of Question" mean and where do they come from. I also do not understand why my solution doesn't work.

Can you please explain the solution to me in easy language?