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Taanis Bechoros-Fast of the first born:
The custom and date of the fast:
On every Erev Pesach, it is customary for the first-born to fast until nightfall in commemoration of the miracle of them being saved from the plague of death of the firstborns in Egypt. [Practically, today the custom is for all those obligated to fast to participate in a Siyum Misechta and exempt themselves from the fats, as will be explained in C. Nonetheless, one who did not participate in the Siyum Misechta, is obligated to fast as stated above.]
Pesach or Erev falls on Shabbos: When Pesach falls on Shabbos, the firstborns fast on Erev Shabbos, which is also Erev Pesach. When Pesach falls on Sunday, and Erev Pesach falls on Shabbos, then the fast is preceded to Thursday.
If the fast of the first born is pushed up to Thursday, may the firstborn eat before Bedikas Chametz? When Pesach falls on Sunday and the fast of the first born is pushed up to Thursday the 13th, which is Erev Bedikas Chametz, the firstborns who are fasting face a dilemma regarding eating before the Bedika. The following is the ruling: If a Bechor who is fasting has many rooms to check, and it is difficult for him to continue fasting until its conclusion, then he may eat a little prior to performing the Bedika, as only an actual meal was forbidden to be eaten. Alternatively, he is to appoint an emissary to perform the Bedika while he eats.
Who is obligated to fast [or participate in a Siyum to exempt their fast]?
*Being that today the custom is to participate in a Siyum rather than fast, the following Halacha should be viewed as who is obligated to participate in a Siyum in order to exempt their fast, and who is obligated to fast if they could not participate in a Siyum, or have yet to do so.]
Definition of firstborn: Every firstborn has to fast even if he is a firstborn to only parent. Thus, whether he is a firstborn only from his father, or is a firstborn only from his mother he is to fast. A firstborn of one of the parents must fast even if his father or mother is a Levi or Kohen. If one’s mother and father had a miscarriage prior to having their firstborn, he is nevertheless required to fast, as he is still considered a firstborn of his father. If, however, his father already had a child from a previous woman, then he is not considered a firstborn and is not obligated to fast.
Female firstborn’s: There is an opinion who rules that firstborn females also have to fast, as they too were included in the plague. Practically, it is not customary in these countries for first born females to fast.
Oldest of household:  The elders of a family do not fast even if their household does not have a firstborn who is fasting.
A father fasting on behalf of a firstborn who is too young to fast: The custom is that the father fasts on behalf of his son who is a firstborn, if his son is not yet old enough to fast on his own. This is done annually until the son becomes old enough to fast. This applies even if one’s son is only a firstborn from his mother. If the father has two sons who are firstborns, one being his firstborn son, and the second being his wife’s firstborn son, and they are still children, then the fast of the father counts on both of their behalves. If, however, the father is also a firstborn, and must thus fast on his own behalf, it is debated if his fast counts on behalf of his son, as explained next!
A mother fasting on behalf of a firstborn who is too young to fast: If the father is also a firstborn, and must thus fast on his own behalf, then according to some opinions his fast does not count on behalf of his young firstborn son, and rather the mother is to fast on behalf of her son who is a firstborn. Other Poskim, however, rule that the father’s fast counts for also his son even in such a case, and the mother is not required to fast. Practically, the mother is to fast unless doing so poses difficulty, such as it will cause her pain. Certainly she may be lenient not to fast if she is pregnant or nursing. If the mother does not have a husband who is fasting on behalf of her firstborn son, then she is to fast unless she is 30 days after birth, or is pregnant or nursing and doing so will cause her pain. [Practically, it is not customary today for mothers to fast on behalf of their firstborn sons, and they do not even participate in a Siyum. Nevertheless, some who are meticulous do so even today.] Nevertheless, if a mother fasted one time [or joined a Siyum] on behalf of her firstborn son with intent to do this each year until her son becomes old enough to fast on his own, then she must perform Hataras Nedarim to discontinue this practice.
All firstborns, whether from a father or mother, are to fast or participate in a Siyum. A father, who is not a firstborn, is to fast on behalf of a young son who is a firstborn. It is not customary for women to fast even on behalf of their firstborn son, and they likewise are not accustomed to participate in a Siyum, although some who are meticulous do so even today.
Must a first born Chasan within the 7 days of Sheva Brachos fast?
No. He is thus not required to participate in a Siyum.
Must a firstborn convert fast?
It is questionable whether a firstborn convert is required to fast, and thus initially he should try to participate in a Siyum in order to exempt him from the fast without doubt. If he could not do so, he may be lenient to eat food, although should not eat a meal of the five grains [Hamotzi/Mezonos].
Participating in a Seudas Mitzvah, such as a Siyum/Bris:
In lack of a pre-accepted custom, it is permitted for a firstborn to participate in a meal of a Seudas Mitzvah [such as in the meal of a Siyum Misechta, Bris Mila, Pidyon Haben] and thus exempt his fast. Nonetheless, one who is stringent to fast and not rely on a Siyum/Seudas Mitzvah is blessed. In many communities it was accustomed to be stringent to fast and not rely on a Siyum/Seudas Mitzvah, and those who are part of those communities may not be lenient unless they perform Hataras Nedarim. Likewise, anyone who was stringent one year to fast rather than participate in a Siyum, requires Hataras Nedarim to break his custom, if he did so with intent to fast each year. [Practically, the widespread custom today is to participate in a Siyum or other Seudas Mitzvah to exempt the fast. Once one has participated in the Siyum or Seudas Mitzvah, he may now eat the remainder of the day. Nevertheless, one must fast until he participates in the Siyum or Seudas Mitzvah, with exception to the person making the Siyum, who may eat even before the Siyum is made. Likewise by a Bris, the Sandak, father of the son, and the Mohel may eat even before the Bris. It goes without saying, that one who could not participate in a Siyum/Seudas Mitzvah, must fast as stated in A.]
The custom is to participate in a Siyum Misechta, Bris Mila or other Seudas Mitzvah in order to exempt the fast. Nonetheless, the participant is to fast until the Seudas Mitzvah takes place.
Must the participants partake in eating the food offered by the Siyum/Seudas Mitzvah?
Some Poskim rule that one must actually participate in eating the foods provided in the meal that follows the Siyum/Simcha in order to exempt the fast, and simply hearing the Siyum or Bris does not suffice. Other Poskim however rule that by a Siyum, it suffices to simply hear the Siyum, and he may then go home and eat. Practically, it is best for every firstborn to try to eat a Kebeitza of food or drink a Revius during the Siyum, although Bedieved one may be lenient.
May one make a Siyum alone, without any participants?
What is one to do if he has missed all the Siyumim, or does not have one available in his area?
If he is a firstborn, then he must fast. Alternatively, he can study Tractate Tamid and make a Siyum on it that day by himself.
May a Bechor who is sitting Shiva on Erev Pesach go to a Shul to participate in a Siyum?
Some Poskim rule it is forbidden to do so. He is to rather redeem the fast with charity. Other Poskim rule he may go to the Shul and participate in a Siyum Misechta. Alternatively, the Siyum is to take place in his house.
The laws of a Siyum Misechta:
The making of a Siyum: When one completes a Misechta, it is a Mitzvah to rejoice and hold a [public] festive meal for the occasion. [One may make several meals, throughout several days, in honor of the Siyum.]
The status of the meal: The festive meal held for the occasion of a Siyum Misechta is considered a Seudas Mitzvah.
When to finish the Misechta and make the Siyum: Upon reaching the end of a Misechta, one is to leave a small section at the end of the Misechta to be learnt on the day that he plans to make the Siyum and festive meal, thereby completing the Misechta on that occasion.
Attendance: It is a great Mitzvah and obligation for others to join the Siyum celebration, and take part in his Simcha, even though they did not complete the Misechta.
The order of the Siyum-Kaddish and Asara Bnei Rav Papa: After completing the final lines of the Misechta, during the Siyum celebration, Kaddish Derabanan is to be recited if a Minyan is present. One is to strive to have a Minyan by the Siyum in order to say this Kaddish. The prayer of [Hadran Alach and] Asara Bnei Rav Papa is recited [before the Kaddish]. [Other prayers are customarily added, including a prayer within the Kaddish Hagadol. The Chabad custom is to recite the regular Hadran Alach, Aseres Bnei Rav Papa, and then go straight to a regular Kaddish Derabanan.]
On which Misechtos can a Siyum be performed?
One may make a Siyum celebration, with a Seudas Mitzvah, after completing any of the following:
Can one make a Siyum if he did not comprehend what he learned?
No. the Siyum can only be made if one understands, to some level, the words that he read [with exception to the Sefer HaZohar]. However, a Siyum may be made if one understands majority of the material, even though some of the material was not understood.
Can one make a Siyum on a later date if he already completed the Misechta?
The Siyum celebration must be made in close proximity to the completion of the Misechta, as otherwise the Simcha dissipates. [In the event that the Misechta was completed many days earlier, seemingly, the Siyum celebration does not have the status of a Seudas Mitzvah. Perhaps, however, if he concluded the last lines only superficially, with intent to study it in greater depth on the day of the Siyum, then this is also valid. Vetzaruch Iyun!]
May one make a Siyum if he learned the Misechta out of order?
May one make a Siyum Misechta if it was studied in parts by several individuals?
Aneinu in Mincha:
A firstborn who did not participate in a Siyum and is hence fasting is to recite Aneinu in his Mincha Shemoneh Esrei.
 Admur 470:1
 Admur ibid; Michaber 470:1; Tur 470; Tosefos Pesachim 108a; ; Rosh 10:19; Miseches Sofrim 21:3
Other opinions: Some Poskim rule it is not necessary to actually fast, but one is to simply avoid eating a meal, such as Hamotzi or Mezonos. [Rav Yechiel, brought in Mordechai and M”B 470:2]
 Admur 470:7
 Admur 470:7; M”A 470:4
 Admur 470:1
 The reason: As in Egypt both types of firstborns were smitten in the plague, as they each have an aspect of the advantage of a firstborn. The firstborn of the father is considered the first born regarding inheritance, while the first born of the mother is considered the firstborn regarding Pidyon Haben. [Admur ibid]
 The novelty here is that even if he is only a firstborn to his mother, and the mother or father is a Kohen or Levi in which he is exempt from Pidyon Haben, nonetheless, he is included as a first born regarding the fast. The reason for this is because he is still in truth a first born, and it is just that the Torah exempted him from needing a Pidyon. [See Admur ibid]
 Admur 470:2
The reason: As although he is not considered a firstborn regarding Pidyon Haben, as he is not Peter Rechem, nonetheless, he is considered a firstborn regarding Nachal, inheritance. [Admur ibid]
 Admur ibid
The reason: As in such a case he is not considered a firstborn regarding any issue, not inheritance, nor Pidyon Haben. [Admur ibid]
 Admur 470:3; Rama 470:1
 Opinion in Michaber 460:1; Aguda 10:91
 The reason: As the entire idea of firstborns fasting is merely a custom, and since the main warning and plague written of in the Torah was only regarding the male firstborns, therefore the females are not accustomed to fast. [Admur ibid; Levush 470]
 Admur 470:3;Tur 470; Ravaya 2:525
 The reason: Although they too were included in the plague since the main warning and plague written of in the Torah was only regarding the male firstborns, therefore elders of the household are not accustomed to fast. [Admur ibid]
 Admur 470:4; Rama 470:2
 Meaning, the father had a child with another woman prior to having this son, who is a firstborn to his mother. However, step-firstborn son would not require the step father to fast. [See Admur ibid]
 Admur 470:4; Chok Yaakov 470:6
 Admur 470:5; Rama 470:2
 1st opinion in Admur 470:5; Rama 470:2
 2nd opinion in Admur ibid; M”A 470:2; Mateh Moshe 561
 Admur ibid; M”A ibid
 Aruch Hashulchan 470:4 that so is custom; Heard from Rav Eli Landau, that we have never seen mothers fast or join the Siyum; So is the custom of the world, seemingly due to the fact that today all women are considered under pain to fast on Erev Pesach and are hence exempt
 See Piskeiy Teshuvos 470 footnote 21 who writes that the mother may be lenient to participate in a Siyum. See also Nitei Gavriel 42:5 who writes the custom is not to fast [see Poskim there in footnote 8] and rather they rely on the fact that the father, mother and firstborn son join the Siyum. In footnote 10 he writes that the Bier Moshe testified that in their home, his father would make a Siyum each year, and many women came to hear the Siyum and then eat.
 Beis Yehuda 2:23
 Shevet Haleivi 8:117; Piskeiy Teshuvos 470:2
 Admur 470:8; M”AA 470:4; Olas Shabbos; Maharash Halevi 3; M”B 470:10
 Igros Moshe 4:69; Minchas Yitzchak 2:93; Likkutei Sichos 17:67; Otzer Minhagei Chabad p. 89; Piskeiy Teshuvos 470:8
 Eretz Tzevi 1:79; Piskeiy Teshuvos 470:6; See Minchas Yitzchak 8:45
 Piskeiy Teshuvos 470:6 footnote 28
 Admur 470:8; Piskeiy Teshuvos 470:6
 See Minchas Yitzchak 9:45; Piskeiy Teshuvos 470:11
 Maharam Brisk 1:133; Mikraeiy Kodesh 2:22; Minchas Yitzchak 9:45 [Lechatchila]; Chazon Ovadia p. 98; Teshuvos Vehanhagos 1:300; See Michaber 568:1
 Beis Avi 2:16; Rav Elyashiv, brought in Piskeiy Teshuvos ibid footnote 58
 Minchas Yitzchak ibid
 Maharam Bris 1:133; Piskeiy Teshuvos 470:11
 See Pnei Baruch 21:11; Piskeiy Teshuvos 470:10
 Yad Shaul 393:3
 The reason: As it is forbidden for an Avel to hear words of Torah during Shiva. [ibid]
 Peri Hasadeh 4:57; Poskim in Piskeiy Teshuvos ibid footnote 52
 Leket Yosher 2:98; Poskim in Piskeiy Teshuvos footnote 53 that may go anytime; Mishmeres Shalom Samech 23 that may go after midday; Rav Fisher in end of Sefer Pnei Baruch
 See Sefer Askinu Seudasa for a full digest on this topic
 Rama Y.D. 246:26; O.C. 551:10; Nimukei Yosef Bava Basra Perek Yeish Nochalin; Shabbos 118b “Abayey said “When we would see a Torah scholar complete a Misechta we would have a celebratory day.”; Midrash Raba Koheles; Midrash Raba Shir Hashirim; Lekach Tov Tzav in name of Pesikta;
 Igros Kodesh 14:374
 Chavos Yair 70 that a meal may be held also the next day, and perhaps even the day later, brought in Pischeiy Teshuvah 246:78; Aruch Hashulchan 246:27
 Rama Y.D. 246:26; O.C. 551:10; Nimukei Yosef Bava Basra Perek Yeish Nochalin; Or Zarua 2:407
 Shach 246:27 in name of Mahram Mintz 2:119; Aruch Hashulchan 246:44 based on Moed Katan 9a; Kaf Hachaim 551:161
 Shach 246:27 in name of Mahram Mintz 2:119; Taz 246:9 in name of Rashal
 Shach 246:27 in name of Mahram Mintz 2:119
 Shach ibid; Maharam Mintz 2:119; Teshuvas Harama in end; Rashal in Yam Shel Shlomo Bava Kama 37; Rav Haiy Gaon, brought in Sefer Haeshkol
The reason: Some suggests that Rav Papa was wealthy, and was accustomed to make a large Siyum for his sons when they would complete a Misechta. The ten sons also correspond to the ten utterances with which the world was created. [Rama ibid] Alternatively, the sons of Rav Papa are mentioned because they all passed away Al Kiddush Hashem during the lifetime of their father, and hence we mention their name Leilui Nishmas. [Zecher Yehoseif on Miseches Brachos]
 Reshimos Devarim of Rav Chitrik 4:219; Directive of Rebbe to Rav Binyamin Althouse; Toras Menachem 4:239 that the Rebbe remarked to Rav Meir Ashkenazi who said the long Kaddish “This is a novelty to me, and I have never seen this done beforehand.”; See also Hisvadyus 5745 3:1700
 Igros Moshe O.C. 1:157; See Rama 669; Askinu Seudasa Miluim 1
 Minchas Pitim Y.D. 246:26; Pnei Yehoshua Brachos 17a; Halef Lecha Shlomo 386; Igros Moshe O.C. 1:157; Teshuvos Vehanhagos 1:300
 See Piskeiy Teshuvos 470:9
 Rama ibid
 Pischa Zuta in name of Hadras Kodesh; Rebbe in meeting with Pnei Menachem of Ger, printed in Hisvadyus 5744 13th Adar Rishon
 Mentioned in Hisvadyos 5749 4:86; 5750 1:97; Rebbe in meeting with Pnei Menachem of Ger, printed in Hisvadyus 5744 13th Adar Rishon
 Rebbe ibid
 Rebbe in meeting with Pnei Menachem of Ger, printed in Hisvadyus 5744 13th Adar Rishon
 Pnei Meivin 103; Betzeil Hachochma 4:99
 Peri Hasadeh 3:91; Binyan Shlomo 59; Betzeil Hachochma 4:99; Afrakasa Deanya 1:154-3; Mentioned in Hisvadyos 5749 4:86; 5750 1:97; See Yabia Omer 1:26
 See Piskeiy Teshuvos 470:9
 Rebbe ibid
 Yabia Omer 1:26
 Beis Avi 2:52; Mishneh Halachos 6:166
 Likkutei Sichos 32:271
 Shearim Hametzuyanim Behalacha 113:10 in name of Tiferes Shmuel 55
 Piskeiy Teshuvos 470:9
 Yabia Omer 1:26
 Afrakasa Deanya 1:154
 See Shach ibid in name of Maharam of Mintz that one who desires to delay the Siyum celebration is to leave some lines unlearned.
 Minchas Yitzchak 2:93; Betzeil Hachochma 2:28
 Kinyan Torah 5:52
 Admur 470:6
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