This problem involves two people. Person A and person B. They can
either always tell the truth, or always lie. When asked, person A
replies that: "At least one of us is a liar." Does person A and B
tell the truth or do they lie?
What I have so far is that person A can either tell the truth or lie. If he tells the truth, then his statement can be expressed by "A$\lor$B", if he lies then it must be given that they are both speaking the truth, which contradicts that he would be a liar. So person A must be speaking the truth.
But if person A is speaking the truth, then person B could be either lying or speaking the truth. Both would still make person A tell the truth.
So how can I figure out whether person B is speaking the truth or not?
Best Answer
$$\begin{array}{cccc} &&&\text{A says}\\ \text{A lies} &\text{B lies}&\text{A or B lies}&\text{A or B lies}\\ a&b&a\lor b&(a\lor b)\oplus a\\ F& F& F& \color{red}F\\ T& F& T& \color{red}F\\ F& T& T& \color{green}T\\ T& T& T& \color{red}F\\ \end{array}$$