Eve:"Doris and I are twins"

Ann: "Doris and Eve are not twins"
Doris: "Ann and I are not twins"
Who are the twins?

Is everyone telling the truth?

No

To determine who the twins are, we need to analyze the statements made by Eve, Ann, and Doris.

Eve claims that she and Doris are twins. Therefore, if Eve is telling the truth, they are the twins. However, if Eve is lying, her statement cannot be true.

Ann states that Doris and Eve are not twins. If Ann is telling the truth, then Eve's statement is false, which means they are not the twins. On the other hand, if Ann is lying, her statement is false, and it means that Doris and Eve are indeed twins.

Doris says that Ann and she are not twins. If Doris is telling the truth, then they are not the twins. However, if Doris is lying, her statement cannot be true.

Since only one of the three statements can be true, we can conclude that Doris and Eve are the twins. Ann's statement is false because if Doris and Eve are twins, then her claim that they are not twins is incorrect.