Villager Logic Puzzle Alternative Answer Question: Each inhabitant of a remote village always tells the truth
or always lies.A villager will give only a “Yes” or a “No”
response to a question a tourist asks. Suppose you are a
tourist visiting this area and come to a fork in the road.
One branch leads to the ruins you want to visit; the other
branch leads deep into the jungle. A villager is standing
at the fork in the road. What one question can you ask the
villager to determine which branch to take?
I was wondering if the following question to the villager would tell me if the right branch for example would take me to the ruins I want.
You are Truthful if and only if the right branch is the correct branch to the ruins, correct?.
What I tried here is to make a truth table. Let $p$ denote the proposition that the villager is truthful and $q$ denote that the right branch is the correct branch. My question should basically be equivalent to $p \Leftrightarrow q?$
$p\quad \quad q \quad \quad p \Leftrightarrow q \quad \quad Response $
$T \quad \quad T \quad \quad T \quad \quad \quad \quad Yes$
$T \quad \quad F \quad \quad F  \quad \quad \quad \quad No$
$F \quad \quad T \quad \quad F   \quad \quad \quad \quad$ Yes
$F \quad \quad F \quad \quad T    \quad \quad \quad \quad$ No
The truthful villager would answer $p \Leftrightarrow q$ truthfully always, however, a liar villager would answer $\neg (p \Leftrightarrow q)$. In either ways, I hear Yes whenever the right branch is actually the direction I want (i.e when q is true).
Is there any flaws in this answer?

No. There are no flaws in the answer, assuming that the villager understands that "if and only if" implies a material equivalence relation rather than a pair of strict conditionals. See also the following discussion: 
Noah Schweber (https://math.stackexchange.com/users/28111/noah-schweber), Difference between biconditional and logical equivalence, URL (version: 2018-02-14): https://math.stackexchange.com/q/2650472
