1) RELYING ON "BEREIRAH" TO CHOOSE A SHEEP TO CORRESPOND TO THE DOG RETROACTIVELY
QUESTION: The Gemara attempts to prove that "Ein Bereirah" from a case in which two partners divided their jointly-owned property. One took ten sheep, and the other took nine sheep and one dog. Since there is one unidentified sheep in the first partner's portion that corresponds to the dog in the second partner's portion, all of the sheep of the first partner are considered "Mechir Kelev" and may not be offered as Korbanos. The Gemara proves from here that "Ein Bereirah," because if Bereirah would work, then the owner of the ten sheep should be able to designate one of his sheep as the one that corresponds to the dog (Mechir Kelev) and the rest would be permitted as Korbanos.
However, even if Bereirah would work, how would it work here to designate which sheep is the Mechir Kelev? Since all of the sheep are equal in value, how can choosing a sheep now determine retroactively that this was the sheep that was given in place of the dog?
ANSWER: TOSFOS (DH li'Vror) answers that if Bereirah works, then indeed designating one sheep to correspond to the dog is effective, because Bereirah depends on the person's own decision. Since he initially intended to designate as the Mechir Kelev an animal that he would choose later, Bereirah works to clarify that the animal that he chooses later is indeed the one that was designated originally to correspond to the dog.
2) THE EXEMPTION OF A "TEREIFAH" FROM "MA'ASER BEHEMAH"
QUESTION: The Mishnah states that a Tereifah is not included in the count of animals for Ma'aser Behemah. The Gemara (58b, as cited by Rashi here) derives this from a verse (Vayikra 27:32).
This Halachah, however, seems to contradict another Halachah. The Mishnah later (58b) states that when an animal that was counted for Ma'aser Behemah jumped back into the herd of animals that were not yet counted, the entire herd is absolved from Ma'aser Behemah. TOSFOS in Bava Metzia (6b, DH Kafatz) asks that the animal that was counted should be Batel b'Rov, annulled by the majority of animals that were not yet counted, and they should be obligated in Ma'aser Behemah.
The ROSH there answers that the Mitzvah to separate Ma'aser from one's animals requires that the tenth animal be an "Asiri Vadai" -- a definite tenth (that is, the animal being taken as the tithe must come from a group of animals that are definitely obligated to be tithed). An obligation based on a Rov is not sufficient.
If a Rov is not sufficient to effect an obligation of Ma'aser Behemah, then how can any group of animals ever be subject to the obligation of Ma'aser Behemah? The only basis to assume that any animal is not a Tereifah is a Rov that most animals are not Tereifos (see Chulin 11a). If a Tereifah is exempt from Ma'aser Behemah, then a more powerful proof that the animals are not Tereifos is necessary in order for the animals to be obligated in Ma'aser Behemah! (REBBI AKIVA EIGER)
ANSWER: The HAFLA'AH in Kesuvos (15a) establishes an important principle. When the concept of Rov is utilized to resolve one doubt, with respect to the resolution of subsequent doubts the initial resolution based on Rov is considered a Vadai, definite, resolution. Accordingly, once the Rov determines that an animal is not a Tereifah with regard to one matter, such as permitting it to be slaughtered and eaten, we may assume that it is definitely not a Tereifah with regard to other matters, such as Ma'aser Behemah.
3) OFFERING AN ORPHANED ANIMAL AS A KORBAN
QUESTION: The Mishnah states that a Yasom is not included in the count of animals for Ma'aser Behemah. The Mishnah explains that a Yasom is an animal whose mother died or was slaughtered before the baby was born. The Gemara derives this law from the verse (Vayikra 22:27) that teaches which animals are fit to be offered as Korbanos in the Beis ha'Mikdash. The law that a Yasom is invalid is derived from the words, "Tachas Imo," which teach that the baby must live for seven days "with its mother" before it is fit to be offered as a Korban from the eighth day and onwards. A Yasom does not qualify as "with its mother" because its mother died before it was born.
Why is the fact that a Yasom is invalid as a Korban mentioned only here, with regard to Ma'aser Behemah? It should have been mentioned in Zevachim (71a-b, 112a-b), where the Mishnah gives a long list of animals that are unfit to be offered as Korbanos. Why do those Mishnayos not mention Yasom? Similarly, the Mishnayos in Temurah (17a and 28a) enumerate other animals that are invalid as Korbanos, but it makes no mention of Yasom. Why is the Mishnah here the only Mishnah that mentions the Halachah that an orphaned animal is invalid as a Korban?
(a) The TOSFOS YOM TOV answers that there is another animal invalid as a Korban which the abovementioned Mishnayos do not list: the "Nidmeh." RASHI (DH Nidmeh) explains that a Nidmeh is the offspring of a sheep but has the appearance of a goat (that is, it does not appear to be the same species as its mother). Such an animal is unfit to be offered as a Korban. Since the other Mishnayos omit Nidmeh, they also omit Yasom, in accordance with the principle of "Tana v'Shayer" -- the Mishnah does not always include every possible case (see end of Bava Kama 15a).
However, as the Tosfos Yom Tov points out, this answer is problematic, because the Mishnah here also omits Nidmeh, and we do not know of any other animal that is invalid as a Korban that the Mishnah here omits. The Mishnah never omits a single case ("Mai Shayer d'Hai Shayer"); the principle of "Tana v'Shayer" applies only when the Mishnah omits two or more cases from its list.
(b) The Tosfos Yom Tov therefore suggests another answer. The RAMBAM (Hilchos Isurei Mizbe'ach 3:11) lists fourteen different types of animals that are unfit as Korbanos. The RA'AVAD criticizes the Rambam for not mentioning an animal that was born after its mother was slaughtered. The MAHARI KURKUS explains that the reason why the Rambam omits Yasom is that it is included in the category of Yotzei Dofen (an animal born through a Caesarian section), which the Rambam does mention. A Yotzei Dofen is invalid because it is not considered an animal that underwent a normal birth. (The Gemara here derives from the words, "When it shall be born" (Vayikra 22:27), that an animal is fit to be a Korban only when it was born in a normal way.) Similarly, a Yasom is unfit because it was not born in a normal way; being born after the death of its mother is not a normal birth. The Mahari Kurkus cites the Gemara in Chulin (38b) that indeed states that if the mother died and then the baby was born, the baby is unfit to be offered as a Korban because of the verse, "When it shall be born."
The only case of a Yasom that is not included in the category of Yotzei Dofen, but instead is derived from "Tachas Imo," is the case of a baby animal born at the exact moment that its mother died. However, since the Halachah follows the view of the Chachamim in the Mishnah earlier (17a) who maintain "Iy Efshar l'Tzamtzem" (it is impossible for two natural events to occur simultaneously), it could be that the verse that excludes this type of Yasom refers exclusively to a case in which Eliyahu ha'Navi comes and reveals that the baby was born at the precise moment that the mother died. (This approach, in fact, is mentioned by TOSFOS to Chulin 38b, DH Ela Zeh.)
Based on the explanation of the Mahari Kurkus, the Tosfos Yom Tov answers that perhaps the reason why the Mishnayos elsewhere do not mention Yasom is that Yasom is always included in Yotzei Dofen, except for the theoretical case in which it is born at the exact moment that its mother dies. Because such a case might exist, the Mishnah here mentions the case of Yasom. It is not mentioned in the other Mishnayos because they are discussing the laws of Korbanos in general. If one Mishnah would mention Yasom, then all of the Mishnayos that discuss Korbanos would have to mention it as well. In contrast, the Mishnah here is discussing the laws of Ma'aser Behemah, which differs from other Kodshim, and thus the Mishnah here finds it appropriate to make a single mention of this unusual case of Yasom. (See also RASHASH.) (D. BLOOM)
4) "SHALOSH GERANOS" FOR "MA'ASER BEHEMAH"
QUESTION: The Mishnah teaches that there are three periods during the year with regard to Ma'aser Behemah. RASHI (DH Shalosh) explains that when these times arrive, it is Asur mid'Rabanan to slaughter and eat one's animals until they have been tithed. Prior to the arrival of these times, however, one may slaughter and eat his animals l'Chatchilah. As long as he has not declared the animal to be Ma'aser Behemah, the animal is not sanctified and is permitted.
Is there any deadline mid'Oraisa for fulfilling the obligation of Ma'aser Behemah? If there is no deadline mid'Oraisa, then what prevents a person from using his animals and postponing the fulfillment of the obligation of Ma'aser Behemah indefinitely?
(a) The CHAZON ISH (Bechoros 27:3) explains as follows. The Mitzvah of "Bal Te'acher" forbids one from delaying the offering of any Korban (such as freewill offerings that one pledged to bring) past the first Yom Tov (Pesach, Shavuos, or Sukos) that arrives after one pledges to bring the Korban. One who delays bringing his Korban past the first Yom Tov transgresses the Mitzvas Aseh of "va'Haveisem Shamah" (Devarim 12:6; Rosh Hashanah 4a-b), and if he delays bringing it for three Regalim, he has transgressed the Lo Sa'aseh of "Lo Se'acher l'Shalmo" (Devarim 23:22).
Similarly, the Mitzvos of "va'Haveisem Shamah" and "Lo Se'acher" require that Ma'aser Behemah be separated by the first Yom Tov that arrives after the birth of this group of animals. The obligation to separate Ma'aser Behemah does not prevent one from selling or using the animals prior to the Yom Tov, because selling an animal exempts the animal from Ma'aser before it becomes obligated. If three Regalim pass and the owner of the animals does not separate Ma'aser Behemah, then he has transgressed the prohibition of Bal Te'acher.
(b) The MELECHES SHLOMO (Shekalim 3:1) quotes RAV SA'ADYA (a commentator on the Mishnah) who explains that the deadline for Ma'aser Behemah according to Torah law is Rosh Chodesh Elul, since this is the "Rosh Hashanah" for Ma'aser Behemah, as the Mishnah in Rosh Hashanah (2a) teaches.