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The reason for the fast
Which firstborns are obligated to fast?
- A firstborn of one’s mother or the firstborn of one’s father (or both) should fast on Erev Pesach. The reason is that Hashem killed both the firstborns of the father and of the mother in Egypt. 
- Even a Levi or Cohen should fast.
- A groom within 7 days of the wedding doesn’t have to fast on Tanit Bechorot.
- A firstborn born through a caesarian section or firstborn after a miscarriage should also fast.
- The Ashkenazic minhag is that women don’t fast.  This is also the Sephardic minhag. Even for those who the custom is for women to fast, if the woman is pregnant or nursing she shouldn't fast. 
- A father should fast in place of his son who is a firstborn but is under Bar Mitzvah. According to the minhag to listen to a Siyum, the father should go to the Siyum in place of his son. 
- If the firstborn child isn't yet 30 days old the father doesn't have to fast or listen to a siyum but if it is possible to do so he should.
- The Rama writes that if the father is a firstborn, the mother should fast for her firstborn son who is under Bar Mitzvah. However, the Mishna Brurah quotes some poskim who say that the father's fast counts for the son as well. Therefore, the Mishna Brurah allows a mother to be lenient if she is in pain. 
- The Aruch HaShulchan writes that we no longer have the minhag that a parent should fast for a firstborn son who is under Bar Mitzvah. 
- If the father is a firstborn and also has a young son who is a firstborn, it is sufficient for the father to hear a siyum for both of them.
Those who are unable to fast
- One who has an ache in his eyes or head is not required to fast. 
- If someone will only be able to eat a very small amount because of the fast and won’t be able to fulfill the mitzvot of Matzah and 4 cups of wine, one shouldn’t fast. Nevertheless, it is preferable that he just have snacks and not a meal. 
Tanit Bechorim on Friday and Shabbat
- If Erev Pesach falls out on Shabbat, some say that one is not obligated to fast, while others say that one should fast on Thursday. The minhag follows the latter opinion. The minhag is to do a Siyum on Thursday and exempt oneself from the fast, even those who fast Tanit Bechorot regular years. Some say it’s preferable to make a Siyum on Friday in addition to the one on Thursday.
- If Erev Pesach falls out on Friday, the fast should take place on that day. 
Minhag to join a Siyum
See the Siyum Masechet page for more details
Regarding the Coronavirus Pandemic, see Halachot Related to Coronavirus, Taanit Bechorot
- Many are lenient to join in a Siyum Masechet and to hear the end of the Masechet and the Siyum and then join for the Seudat Mitzvah and break the fast the rest of the day. 
- Some say that it’s critical to understand the last piece of Gemara to join for the Siyum, however, the minhag is to be lenient in any circumstance.  Some say that one only has to participate in some of the learning, maybe by hearing the rabbi speaks words of mussar. 
- Preferably, after hearing the Siyum one should eat a KeBaytzah of Mezonot or bread as a meal for the Siyum. Some are lenient and allow one to break the fast after hearing a Siyum without eating there. 
- If a woman finishes a complete masechet she still cannot absolve the first borns from the fast. 
- Since someone within the seven-day mourning period may not attend such a celebration, he wouldhave to fast Taanit Bechorot. If he is weak and fasting through the day would adversely affect his ability to perform the mitzvot of the seder night, he may redeem himself from the fast by giving some money to charity.
- Some say a child's siyum can exempt an adult from fasting Taanit Bechorot.
- Mishna Brurah 470:1, Kaf HaChaim 470:1, Tur 470:1. The original source for this fast is Masechet Sofrim 21:3. Kaf Hachayim 470:30 explains that even though the miracle happened on the fifteen we fast on the fourteenth because we don't fat on yom tov.
- Shulchan Aruch O.C. 470:1
- Mishna Brurah 470:2, Kaf Hachayim 470:2.
- Mishna Brurah 470:2
- Kovetz MeBet Levi (Nissan 5761 pg 86). Rav Ovadia Yosef in Yabia Omer 1:25 says he should try to participate in a seudat mitzva.
- Guide to Practical Halacha (v. 5 p. 142 n. 4-5) quoting the Debrecener
- Rama 470:1, Mishna Brurah 470:4
- Although Shulchan Aruch O.C. 470:1 holds that women firstborns should fast Tanit Bechorot and Rav Ovadia Yosef in Sh”t Yechave Daat 3:25 and Sh”t Yabia Omer 4:42 upheld that minhag, nonetheless, in Chazon Ovadia Pesach p. 207-8 he concluded that it wasn't the minhag today. Rav Shlomo Amar in Haggadah Myamim Yamim agrees. Kaf HaChaim 470:17 quotes the Chida (Machazik Beracha 470:2) and Ben Ish Chai (Parashat Tzav) that the Sephardic minhag is to follow the Rama that women do not fast Tanit Bechorot.
- Mishna Brurah 470:9, Kaf Hachayim 470:15 and 21.
- Rama 470:2, Piskei Teshuvot 470:6, Yalkut Yosef 470:19, Yosef Daat (Dinei Chinuch 16:3)
- Yalkut Yosef 470:19
- Rama 470:2
- Mishna Brurah 470:9
- Aruch HaShulchan 470:4
- Rav Hershel Schachter (YIW Packet) held that it is sufficient for the father to hear the siyum for himself since it is a stringency anyway for the son to have to hear the siyum. He said that is the minhag unlike the Nitai Gavriel 2:42:5 quoting the Beer Moshe who held that it is necessary for the father to listen to a siyum for himself and the mother to hear a siyum for herself.
- Mishna Brurah 470:2
- Mishna Brurah 470:2
- Shulchan Aruch and Rama O.C. 470:2
- Sh”t Igrot Moshe 4:69 writes that it’s sufficient to make a Siyum on Thursday and Piskei Teshuvot 470:4 writes that such is the minhag. Rabbi Dovid Heber agrees. Sh"t Yechave Daat 1:91, Chazon Ovadyah Pesach pg 100, and Or Letzion 3:12(2) write that even though the strict law is that the firstborns are exempt it's preferable that they join in a Siyum. See Birkei Yosef 470:2 who quotes the Meiri who says that if Erev Pesach is on Shabbat, one should fast Tanit Bechorot on Friday.
- Sh”t Elef Lecha Shlomo 1:386
- Sh”t Teshuvot Vehanhagot 2:111, Sh”t Mishneh Halachot 7:65, Orchot Rabbenu (vol 2 pg 57), Rav Hershel Schachter ("Inyanei Erev Pesach She'chal BeShabbat", min 71-72). Rav Hershel Schachter (YIW Packet) thought that it was only a stringency and according to the halacha is sufficient to listen to a siyum on Thursday.
- Mishna Brurah 470:5, Chazon Ovadyah Pesach pg 101 (5763 edition, pg 117)
- Yalkut Yosef, 470:16, Mishna Brurah 470:10, Piskei Teshuvot 470:6, 8 based on Igrot Moshe 4:49, Maharsham 215, Ben Ish Chai Tzav 25, Kaf Hachayim 470:10 and Aruch HaShulchan 470:5
- Piskei Teshuvot 470:10
- Rabbi Eli Mansour Dailyhalacha
- Piskei Teshuvot 470:11, Halichot Shlomo 8:1
- Rabbi Eli Mansour Dailyhalacha
- Yalkut Yosef 470:24
- Shu"T BeTzel HaChochmah 4:100. The following summary appears on Mi Yodea: "Rabbi B'tzal'el Stern (B'tzel Hachochma volume 4 number 100) was asked whether a minor's siyum exempts an adult from taanis b'choros. He cites the Rambam (Hilchos Korban Pesach 5:7) as saying that someone who became an adult between Pesach and Pesach sheni need not offer the korban pesach sheni. The explanation of this Rambam is that, because the Torah says to include an entire household, including children, on the first pesach offering, it's as though the then-child fulfilled the mitzva just like an adult (even though normally we say children are exempt from mitzvos). Rabbi Stern extends this to Torah study: because a parent has a Torah obligation to teach his son Torah, it's as if the son has fulfilled a mitzva by studying Torah just like an adult. Therefore, Rabbi Stern concludes, his siyum can be used to exempt an adult from taanis b'choros.
This follows Rabbi Stern's understanding of the Kesef Mishneh (ad loc., citing Rabbi Yosef Kurkus) and Mabit (קרית ספר, ad loc.), that the father's obligation to include his minor son in the korban pesach essentially allows an adult-level fulfillment of the obligation by the son. An alternative understanding of the Kesef Mishneh is expounded by Rabbi Chaim Soloveitchik. He argues that there are two legal aspects to the fulfillment of the korban pesach commandment. The first is the individual's obligation to perform a commandment, and the second is the legal completion of the sacrificial service. Rabbi Soloveitchik contends that only the second aspect of the korban pesach applies to a minor, so the minor's parent is capable of including him in a household group for the korban's consumption. Since the korban pesach service could be performed by a minor, its prior performance has legal significance for him once he reaches the age of majority. However, it is not as if he actually fulfilled an obligation as a minor."