Kiddushin, Chapter Three, Mishnah Ten
This mishnah and the next one deal with cases where a man says that he betrothed a certain woman and she contradicts him or where she claims that he betrothed her and he denies it.
The general principle upon which this mishnah stands is that a person can make a statement which impacts himself/herself but does not impact others. Stated otherwise, a person is believed with regard to personal consequences but not with regard to consequences to others.
1) If he says to a woman, I betrothed you, and she says, You did not betroth me: he is prohibited to her relatives, but she is permitted to his relatives.
2) If she says, You betrothed me, and he says, I did not betroth you, he is permitted to her relatives but she is prohibited to his relatives.
3) I betrothed you, and she says, You betrothed my daughter, he is forbidden to the relatives of the senior [the mother], but the senior is permitted to his relatives; he is permitted to the juniors [the daughters] relatives, and the junior is permitted to his relatives.
Section one: The man claims he has betrothed the woman, and therefore he is believed with regard to himself. The consequence is that all of the womans relatives (daughter, mother, sister etc.for a full list see Yevamot 4:7) are prohibited to him, because according to him, he is betrothed to their relative. However, the woman denies that this man betrothed her. Hence she is not prohibited to his relatives.
Section two: This is the opposite case. Since she claims to be betrothed to him, she is prohibited from marrying his relatives. Since he denies being betrothed to her, he is permitted to her relatives.
Section three: The mishnah adds a wrinkle to the previous cases. Here the husband claims that he betrothed a woman and she responds that he didnt betroth her but rather he betrothed her daughter (again, one can imagine a Hollywood scenario lurking behind this mishnah!). As above, he is prohibited to her relatives because he claims that he betrothed her. The mother (the senior woman) is not prohibited to his relatives, because she claims that she is not betrothed to that man. The man is not prohibited to the daughters relatives because he denies having betrothed her. The daughter is also permitted to his relatives, since she didnt claim that she was betrothed to him, but rather the mother did. A mother does not have the legal ability to give her daughter in betrothal and hence, unlike a father who does have such a legal ability, she is not believed to say that she has done so.