1) THE FUNCTION OF "BITUL B'ROV"
QUESTION: The Gemara quotes the Mishnah in Parah (9:1) which discusses a case in which a drop of regular water falls into a bowl of Mei Chatas (the consecrated water which contains the ashes of the Parah Adumah and which is used for the purification process of one who became Tamei with Tum'as Mes). Although there clearly is a majority of Mei Chatas, may this water be used in the purification process of one who is Tamei? Rebbi Eliezer rules that if two sprinkles from this water are administered, then it may be used to make a person Tahor. The Chachamim argue and rule that this water may not be used. The Gemara discusses both opinions at length.
Why does the Mishnah in Parah not take into account the fundamental principle of Bitul b'Rov (as discussed earlier, on 78b)? This is a case of Min b'Mino (water fell into water) to which Bitul b'Rov applies, and the drop of ordinary water should be nullified by the majority of Mei Chatas! Even Rebbi Eliezer, who rules leniently in this case, seems to ignore the logic of Bitul b'Rov.
(a) TOSFOS (79b, DH Tenan Hasam) answers that the law in the Mishnah in Parah (either the ruling of Rebbi Eliezer or the ruling of the Chachamim) certainly is mid'Rabanan. The Rabanan instituted a stringency with regard to Mei Chatas because of the severity of the laws of Tum'ah and Mei Chatas. Mid'Oraisa, however, the ordinary water indeed is Batel b'Rov.
(b) The RIVA, quoted by the CHOK NASAN, argues that the rule of Bitul b'Rov does not apply in this case. Bitul b'Rov does not mean that the minority in the mixture acquires the status of the majority. Rather, it means that the minority does not interfere with the status of the majority; the minority is ignored. Accordingly, even if Bitul b'Rov would apply, the regular water which would be sprinkled from this mixture would not have the status of Mei Chatas and would not purify the person. This makes the entire mixture Pasul.
The logic used by the Riva is attributed to the ONEG YOM TOV (OC 4). He uses this principle when he asserts that Tzitzis that were spun without specific intent to use them for the Mitzvah of Tzitzis may not be added to a majority of strings that were spun with the correct intention by applying the principle of Bitul b'Rov. Since they do not attain the status of the majority, they do not add to the correct amount of valid Tzitzis required. The YAD BINYAMIN adds that a similar line of reasoning is advanced by the RAN in Nedarim (59a), who states that a permitted substance which is the minority of a mixture retains its status even though the majority of the mixture is a forbidden substance. It seem that the Ran maintains that something which is a minority retains its status even though it is Batel b'Rov.
However, the CHAMUDAS DANIEL points out that this principle is challenged by many other Rishonim. As mentioned earlier, Tosfos explicitly maintains that Bitul would work in this case. Tosfos clearly maintains that the regular water in the mixture indeed becomes Mei Chatas because of Bitul. This is also apparent from Tosfos in Bava Metzia (6b, DH Kafatz), who questions the Gemara's statement that if an animal that was separated as Ma'aser Behemah jumps back into the area where the animals that were not yet counted are gathered, all of the animals are exempt from Ma'aser Behemah. Tosfos asks why this should be: why does Bitul b'Rov not apply so that all of the animals in the mixture are considered as obligated to have Ma'aser separated from them? From the question of Tosfos there it is evident that he maintains that the animal that was Ma'aser Behemah loses its status once it becomes Batel in the majority of animals from which Ma'aser was not separated. The SHITAH MEKUBETZES (Hashmatos to 78b), in his third explanation, also expresses clearly that a minority of Isur turns into Heter (see also SHALOM RAV to 78b in the name of the DARCHEI YOSHER
The Chamudas Daniel therefore concludes, unlike the Oneg Yom Tov quoted above, that a majority of Tzitzis strings that were made with intent for the Mitzvah of Tzitzis turn the minority of strings that were made without the proper intent into valid strings, enabling the person to fulfill the Mitzvah of Tzitzis with them. (See also KOVETZ HE'OROS, Yevamos #59, who discusses this argument.) (Y. MONTROSE)
2) HOW MANY "ZERIKOS" ARE PERFORMED WHEN THE BLOODS OF DIFFERENT TYPES OF KORBANOS BECOME MIXED
OPINIONS: The Mishnah (80a) discusses three cases in which the bloods of separate Korbanos become mixed together: a mixture of two Korbanos, each of which requires only one Zerikah; a mixture of two Korbanos, each of which requires four Zerikos; and a mixture of a Korban which requires one Zerikah with a Korban that requires four Zerikos. The Mishnah states that in the first case "they should be given with one sprinkling."
The Gemara asks that, assuming that each drop of blood is not considered a mixture of both Korbanos, how can one be assured that the blood from both Korbanos reached the Mizbe'ach? Perhaps all of the blood that was placed on the Mizbe'ach was from only one Korban. (See TOSFOS, DH Kegon, who understands the Gemara's question differently.) The Gemara answers that the Mishnah refers to a case in which "one [sprinkle of blood] became mixed with one [sprinkle of blood]." What does the Gemara mean by this answer?
(a) RASHI (DH Achas b'Achas) explains that the Gemara means that the Kohen places all of the blood that became mixed onto the Mizbe'ach, thereby ensuring that some blood from each Korban is placed on the Mizbe'ach. The Gemara's initial assumption was that the Mishnah means that only a single Matanah is performed, because no matter how much blood is in the mixture, each drop is considered a mixture of the blood of both Korbanos. However, according to the opinion that each drop of blood is viewed as the blood from only one animal and not as a mixture of blood from both animals, the Mishnah must mean that enough blood for one Matanah from each animal became mixed together, and by placing the entire mixture on the Mizbe'ach the Kohen certainly performs Zerikah for both animals. Rashi apparently understands that the Mishnah's statement that "they should be given with one sprinkling" means, as the Gemara initially assumes, that one Matanah should be performed. The Gemara's answer is that this wording also means that one must give an amount of one Matanah from each Korban, and not the total amount of only one Matanah.
(b) The SHITAH MEKUBETZES (Hashmatos #8) has difficulty with Rashi's explanation. In the Mishnah's third case, in which a Korban that requires one Zerikah becomes mixed with a Korban that requires four, the Gemara seems to retract the explanation used in the previous two cases. Rashi (81a, DH v'Chi Teima) explains that the Gemara means that Rebbi Eliezer's opinion in the Mishnah ("Yinasnu b'Matan Arba") cannot mean that five Zerikos should be given. The Shitah Mekubetzes asks, how can the Gemara even entertain such a possibility? According to the Gemara's original understanding, one might have understood this to mean that either four Zerikos must be performed, or eight, but not five! There is no way that the wording of the Mishnah could possibly mean five Zerikos.
The Shitah Mekubetzes therefore gives a different explanation (in the name of "Mori"). He explains that when the Mishnah says, "Yinasnu b'Matanah Achas," it means that the total amount of blood that the Zerikos of both Korbanos required before they were mixed together should be given in as many Matanos as the Mishnah says. For example, "Yinasnu b'Matanah Achas" means that the amount of two Zerikos, one from each Korban, should be sprinkled on the Mizbe'ach at one time. Therefore, when the Gemara says that one cannot learn that Rebbi Eliezer means five Zerikos, it does not mean that "Matan Arba" in some way means five Zerikos. Rather, it means that the amount of blood required for the Zerikos of both Korbanos, indicated by the word "Yinasnu," should be given in four Zerikos.
The Shitah Mekubetzes also disagrees with Rashi about how much blood the Gemara is discussing. According to his explanation, when the Gemara says that in the Mishnah's case, "one became mixed with one," it does not necessarily mean that the amount of one Zerikah is mixed with the amount of only one other Zerikah. It means that the amount of the Zerikah is comprised of the amount of blood which was supposed to be given for both Korbanos. (Y. MONTROSE)