Mishnah 10 in the third chapter of Kiddushin deals with a dispute between a man and a woman as to whether kiddushin took place between them, and with the consequences of that dispute regarding the prohibition of each side's relatives to the other.
The first case - he claims and she denies:
"Ha'omer le'ishah kidashtich, vehi omeret lo kidashtani - hu asur bikrovoteha vehi muteret bikrovav" - one who says to a woman, "I betrothed you," and she says, "You did not betroth me," he is forbidden to her relatives and she is permitted to his relatives.
He is forbidden to her relatives - according to his claim she was his wife, and therefore her relatives - her sister, her mother and her daughter - are forbidden to him. This prohibition remains in force even if he gives her a get.
And she is permitted to his relatives - since according to her words she was never betrothed to him.
The second case - she claims and he denies:
"Hi omeret kidashtani vehu omer lo kidashtich - hu mutar bikrovoteha vehi asurah bikrovav" - she says, "You betrothed me," and he says, "I did not betroth you," he is permitted to her relatives and she is forbidden to his relatives.
He is permitted to her relatives - since according to his words he never betrothed her.
And she is forbidden to his relatives - since according to her words she was betrothed to him.
The novelty of this ruling:
When he is the one claiming that he betrothed her, we do not believe him to the point of forbidding her, since his claim does not involve any significant loss to himself: he becomes forbidden only to her relatives, and he had no plans to marry any of them. It is understandable, then, why she remains permitted to his relatives, for his statement alone does not establish his credibility. But when she claims that she was betrothed to him, she forbids herself to the entire world except for him, and one might therefore have thought that we believe her to such an extent that he too would become forbidden to her relatives. The Mishnah comes to teach us that we do not say this.
The third case - "You betrothed only my daughter":
"Kidashtich, vehi omeret lo kidashta ela et biti - hu asur bikrovot gedolah, ugedolah muteret bikrovav; hu mutar bikrovot ketanah, uketanah muteret bikrovav" - he says, "I betrothed you," and she says, "You betrothed only my daughter," he is forbidden to the relatives of the older woman, and the older woman is permitted to his relatives; he is permitted to the relatives of the younger one, and the younger one is permitted to his relatives.
He is forbidden to the relatives of the older woman (the mother) - since according to his claim she was betrothed to him, even though she denies it.
The older woman is permitted to his relatives - since according to her words she was not betrothed, even though he claims that he betrothed her.
He is permitted to the relatives of the younger one (the daughter) - since according to his words he did not betroth her, even though the mother claims that he did.
The younger one is permitted to his relatives - because the mother is not believed when she says that he betrothed her daughter.
The novelty of this ruling:
Even though by Torah law a father is believed when he says that he betrothed his daughter, we do not say that the Sages extended this law to the mother as well and granted her rabbinic credibility to say that he betrothed her daughter. For this reason her words that the daughter was betrothed to this man are not accepted, and the daughter remains permitted to his relatives in the future.
In summary: in this Mishnah we learned three cases of a dispute about kiddushin: when he claims and she denies - he is forbidden to her relatives and she is permitted to his relatives; when she claims and he denies - she is forbidden to his relatives and he is permitted to her relatives; and when the mother responds that it was not she who was betrothed but her daughter - he is forbidden only to the mother's relatives, while the daughter and his relatives remain permitted to one another, since the mother is not believed in this matter.