Five persons A, B, C, D and E chat:
[list][list][list][list][list]A: “B lies if and only if D is telling the truth.”
B: “If C is telling the truth, then either A or D is a liar.”
C: “E lies, and also A or B lie.”
D: “If B is telling the truth, then A or C too.”
E: “Among the persons A, C and D is at least one liar.”[/list:u][/list:u][/list:u][/list:u][/list:u]
Two persons are lying. Which?
[tab]In your previous post you were saying that A and B were liars, but that is not possible that both A and B are liars. Now you are saying that A and E are liars, but it is also not possible that both A and E are liars.[/tab]
Please try again.
Sanjay, we are supposed to put our answers in a tab so that others don’t see it unless they want to.
And I can see that this puzzle also has a communication issue that depends on interpretation.[tab]A: “B lies if and only if D is telling the truth.”
If that is a lie, all you know is that B is independent of D.
B: “If C is telling the truth, then either A or D is a liar.”
If that is a lie, then if C is telling the truth, both A or D are true.
C: “E lies, and also A or B lie.”
If that is a lie, either E is true or both A or B are true.
D: “If B is telling the truth, then A or C too.”
If that is a lie, then if B is telling the truth, both A and C are lies.
E: “Among the persons A, C and D is at least one liar.”
If that is a lie, A, C, and D are true.[/tab]
Communication comes before attempts at logical deduction. Different people read the same words to mean different things. Thus logic is only flawless if the words are understood as intended (often not the case). In logic, the nuances of language can be critical.