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In order to reconcile the dispute between Beis Shamai and Beis Hillel, Rebbi Yochanan ben Nuri attempted to institute a decree that a Tzaras Ervah do Chalitzah. However, the decree was not carried out. (1)
The daughter of Raban Gamliel was married to his brother and he did Yibum with the Tzarah. Acherim say that the reason why the Tzarah was permitted to Raban Gamliel was that his daughter was an Ailonis. (2)
Rebbi Akiva picked an Esrog on the first day of Shevat of the third year of Shemitah, and he separated both Ma'aser Sheni and Ma'aser Ani. (3)
The daughter-in-law of Beis Shamai gave birth prior to Sukos, and Beis Shamai made a hole in the roof above the baby and covered it with Sechach.
There was a hollowed-out rock in Yerushalayim called "Shokes Yehu" that was used for a Mikvah even though it held less than 40 Se'ah of water. It was a valid Mikvah because it was connected to a proper Mikvah by way of a breach in the Mikvah. (4)
Beis Shamai: Olives are not susceptible to Tum'ah even if they are damp. Beis Hillel: Olives are susceptible to Tum'ah unless a perforation is made in the barrel.
Beis Shamai and Beis Hillel agree that if the barrel was perforated and the perforation was blocked by sediment, the olives are not susceptible to Tum'ah.
There were prestigious families in Yerushalayim that married off the Tzaros of an Ervah without Chalitzah, and some of the children served as Kohanim Gedolim.
Rebbi Yehoshua is of the opinion that only a child born from a prohibited relationship punishable with Misas Beis Din has the status of a Mamzer.
A child born from a relationship that is prohibited with a Lav is valid for Kehunah, with the exception of a child born from a relationship between a Kohen Gadol and a widow. (5)
A BIT MORE
1. Raban Shimon ben Gamliel was concerned of the effect that the decree would have on the Tzaras Ervah who already married without Chalitzah. If we now would require them to do Chalitzah, it would tarnish the reputation of those who did not. We do not want to institute a decree that will tarnish a wife's reputation to her husband, because "the ways of the Torah are pleasant."
2. The Tana Kama agrees with Acherim that the daughter was an Ailonis. However, the Tana Kama maintains that the brother was not aware that she was an Ailonis, thus making the marriage to the daughter a Mekach Ta'us. That is why Raban Gamliel was permitted to the Tzarah. Alternatively, the daughter was divorced after the brother married the Tzarah. The Tana Kama maintains that the Tzarah is permitted as a result of the divorce, and Acherim maintain that only if the daughter was divorced prior to the marriage of the Tzarah would the Tzarah have been permitted to Raban Gamliel. Alternatively a condition was stipulated at the marriage of the daughter and the condition was not upheld. The Tana Kama maintains that the marriage was invalidated, and Acherim maintain that the condition no longer applied once they had marital relations.
3. Ma'aser Sheni is separated from the produce of the second year while Ma'aser Ani is separated from the produce of the third year. Beis Shamai holds that the first of Shevat is Rosh Chodesh for trees and thus it is the beginning of the third year while Beis Hillel holds that the fifteenth of Shevat is Rosh Chodesh for trees and thus it was still the second year.
4. According to Beis Hillel the breach only needs to be the size of a tube in a leather flask and according to Beis Shamai the breach must be the majority of the wall of the Mikvah.
5. The Gemara teaches a Kal va'Chomer: If a child born from a relationship between a Kohen Gadol and a widow is invalid for Kehunah even though a widow is forbidden only to a Kohen Gadol, then certainly a child born from other relationships that are prohibited with a Lav should be invalid for Kehunah. However, the Kal va'Chomer is refuted because of the fact that a widow to a Kohen Gadol is different because the widow herself becomes invalid for Kehunah.
THE MITZVAH OF CHINUCH ACCORDING TO BEIS SHAMAI
The Beraisa says that the daughter-in-law of Beis Shamai gave birth prior to Sukos, and Beis Shamai made a hole in the roof above the baby and covered it with Sechach. Rashi explains that Beis Shamai maintains that a child who still needs his mother is required to sit in the Sukah. The question is that the Mitzvah of Chinuch cannot possibly apply to a newborn baby. Even though Beis Shamai says that a child who still needs his mother is required to sit in the Sukah, that is only in order to train him for the Mitzvah; that does not apply to a child who is too young to be trained. The Chochmas Shlomo answers that besides the newborn baby, there was another child who was five years old in the same room who still needed his mother. The Sechach was put up for the benefit of the five-year-old. Beis Hillel, however, disagrees because if the child still needs his mother, the Mitzvah of Chinuch does not yet apply.
FUSING ONE MIKVAH WITH ANOTHER
If a person wishes to fuse an invalid Mikvah with a valid one, or to fuse two Mikva'os together so that between them they will have the minimum amount of water, the hole that connects them must be at least the size of the tube in the opening of a leather flask, and the water- flow between them must be the width of the breach. Once the two Mikva'os are fused together even for a second they will always be valid, even if the breach immediately becomes closed up. (Shulchan Aruch YD 201:52)
If the hole becomes closed up after the Mikva'os are fused together, they are valid only in a case where an invalid Mikvah was fused with a valid one. However, if a Mikvah that was lacking the minimum quantity of water was fused with a valid Mikvah, once the hole is closed up the Mikvah lacking the minimum quantity of water again becomes invalid. (Shach)
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