Correct option is B
Solution:
Given the information that a liar always lies and a non-liar never lies, let's analyze the options:
"All are liars": This statement contradicts the information given because if all are liars, they would call their left neighbor a liar, but that would mean the person on their left is telling the truth, which is inconsistent.
"n must be even, and every alternate person is a liar": This option is correct. If n is even and every alternate person is a liar, then it can work without logical contradictions. For example:
Person 1 (on the far left) is a truth-teller. Person 2 (to the right of Person 1) is a liar. Person 3 (to the right of Person 2) is a truth-teller. Person 4 (to the right of Person 3) is a liar.
This pattern continues around the table. In this setup, every alternate person is a liar, which means they will always lie and call their left neighbor a liar, while the truth-tellers will always tell the truth and call their left neighbor a liar. There are no logical contradictions in this arrangement.
"n must be odd, and every alternate person is a liar": This option does not work because if n is odd, then there will be an even number of people between any two liars, which means there will be a truth-teller in between. This breaks the condition that every alternate person is a liar.
"n must be a prime": This option does not necessarily hold true. For example, you can have a group of 6 people where every alternate person is a liar, and this satisfies the conditions without n being a prime number.
Conclusion:-
So, the correct answer is option b: "n must be even, and every alternate person is a liar."
