Before us is Mishnah 8 in the third chapter of Maseches Kiddushin, which deals with a father's credibility regarding his daughter. According to the Torah, a father has the right to betroth his daughter while she is a minor - as long as she has not reached the age of bas mitzvah - and also while she is a na'arah, during the six months from the time she became bas mitzvah and produced signs of maturity, until she becomes a bogeres. Once she becomes a bogeres, she has left his authority and he can no longer betroth her.
"Kidashti es bitti" - while she is still a minor:
One who says "Kidashti es bitti" - "I betrothed my daughter" - or "Kidashtiha v'gerashtiha k'shehi ketanah" - "I betrothed her and divorced her while she was a minor," meaning that he betrothed her and received her get on her behalf, and at the moment he says this she is still a minor - he is believed. Since at that moment the halachic authority to perform these acts rests in his hands, he is believed to say that he indeed performed them.
And this has an immediate halachic consequence:
If he said only "Kidashtiha" - she is forbidden to every man, since she is permitted only to that man to whom he betrothed her.
If he said "Kidashtiha v'gerashtiha" - she is permitted to every man, but forbidden to a kohen, for according to his words she is a divorcee.
"Kidashtiha v'gerashtiha k'shehi ketanah v'hi gedolah":
If he said "Kidashtiha v'gerashtiha k'shehi ketanah" - "I betrothed her and divorced her while she was a minor" - and at the moment he says this she has already matured and left his authority, he is not believed. He is not believed to forbid her to a kohen, and even if he said only "Kidashtiha," he is not believed to render her a married woman forbidden to every man.
"Nishbeis ufdisiha":
If he said "Nishbeis ufdisiha" - "She was taken captive and I redeemed her," meaning that she was captured by gentiles and he ransomed her - this statement, were it true, would forbid her to a kohen. Nevertheless, "bein shehi ketanah u'vein shehi gedolah - eino ne'eman" - whether she is a minor or an adult, he is not believed. The reason: the Torah gave him no ability whatsoever to affect the status of a captive woman. He has the power to betroth her and divorce her, and by that route even to forbid her to a kohen, but he has no authority to forbid her to a kohen on account of captivity.
One who speaks at the time of his death:
The Mishnah discusses a case in which we have an established assumption that a man has brothers, on the strength of which his wife is subject to yibum or chalitzah, while regarding the question of whether he has children we know nothing. At the time of his death the man makes statements bearing on this:
"Yesh li banim" - "I have children" - he is believed: This statement does not directly conflict with the assumption we hold regarding the brothers, since on the question of children we had no prior assumption at all. Even though he has brothers, the existence of children - sons or daughters - exempts his wife from yibum, and therefore he is believed, and she is not subject to yibum.
"Yesh li achim" - "I have brothers" - he is not believed: This statement bears directly on the assumption we already hold regarding the brothers and comes to change it, and therefore he is not believed concerning it.
One who betroths "my daughter" without specifying:
A man has several daughters: some of them minors, who have not yet reached the age of bas mitzvah, and some of them bogros, who have already passed the age of twelve and a half, whom he cannot betroth by virtue of a father's rights. The Mishnah deals with a situation in which the adult daughters appointed him as their agent to betroth them, so that beyond his ability to betroth the minors by Torah law, he also has the technical ability to betroth the older ones.
Nevertheless, one who betroths his daughter without specifying - the bogros are not included. Since the father did not identify which of his daughters he intended, the adult daughters are not included in the doubt. Because his obligation, his responsibility and his primary Torah-given ability are directed toward the minor daughters, we assume that he gave them priority, and the doubt - as to which of his daughters he intended in this betrothal - applies only to those daughters who are minors or na'aros.
In summary: In this Mishnah we learned the limits of a father's credibility: he is believed to say that he betrothed his daughter, or that he betrothed and divorced her, as long as she is a minor and within his authority, and he is not believed once she has matured; and he is not believed at all in the claim of "Nishbeis ufdisiha," since the matter is not within his authority. We further learned the law of one who says at the time of his death "Yesh li banim" as opposed to "Yesh li achim," and the rule that one who betroths his daughter without specifying - the bogros are not included in the doubt.