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X says "according to Y, I always lie."   Consider four cases:

Case 1: X = F and Y = F  X lies meaning above statement is false and true statement is according to Y, X tells truth. And we have assumed Y lies so according to statement X lies is true (True).

Case 2: X = F and Y = T X lies meaning above statement is false and true statement is according to Y, X tells truth. And we have assumed Y speaks truth so according to statement X speaks truth (contradiction to our assumption---X lies).

Case 3: X = T and Y = F X speaks truth meaning above statement is true so according to Y, X lies. And we have assumed Y lies so  X speaks truth is true (True).

Case 4: X = T and Y = T X speaks truth meaning above statement is true so according to Y, X tells lies. And we have assumed Y speaks truth so according to statement X lies (contradiction to our assumption---X speaks truth ).

Answer should be (i and iv)

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X = False , now Y also False

since Y is telling Truth that X telling lie.  No Conflict 

X = True, now Y also True

since Y is telling , X is telling lie.  Conflict 

X = False , now Y also True

since Y is telling,  x is telling truth.  So conflict arrise since we assume X is false.

X = True , now Y also False

since Y is telling x is telling truth.  No Conflict 

edited by

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