I'm not sure if I'm right about this, so I'd appreciate a little guidance.
In a remote village, there exists two types of people
Truth tellers who will always tell the truth
Liars who will always lie
One day, a stranger visited the village. He met two of the inhabitants, Jack and Emily. The stranger asked them: "Is anyone of you a liar?". Jack replied: "At least one of us is a liar."
What are Jack and Emily? Truth tellers or liars?
I know I can get the answer with the help of truth tables, but I'm not sure what the intial formula should be for Jack's reply. What I came up with for "At least one of us is a liar" was:
J: Jack is a truth teller
E: Emily is a truth teller
$$\neg(J \lor E)$$
Would you agree?