I've been learning about propositions and truth tables recently and been given examples like "If it is raining I will take my umbrella." P=it is raining Q=i take my umbrella. It's very easy to understand that the compound proposition here is that P=>Q. However, I just got a new one that I don't understand how to turn into a compound proposition because the first part has nothing to do with the second... The riddle goes:
There are three paths into a city, each guarded by a soldier. Be careful because they're all liars.
The first says: "The left-side path will take you to the city. Moreover, if the middle path takes you to the city, so will the right-side path"
The second says: "Neither the left-side path or the right-side path will let you into the city"
The third says: "The left-side path will take you to the city, the middle path will not."
So if there are propositions g,m,s and g is the proposition "the left-side path takes you to the city" (same for m and s). Then how do you write compound propositions for each of them?
I had a shot at the first: g^s=>m but then what do I do with this. If the centaur is lying does that mean (g^s=>m) is FALSE?
I don't know why they're asking us for truth tables and compound statements! Logic alone says it's the right-side path!
PS. So to get the right path, I just have to get a truth table where (c1^c2^c3) is true right? And then going back to the far left column where it's just g,s,m - one of them should be T and that's the right path?