Gemara

(Mishnah): If one did a Melachah, and he does not know if it was on Shabbos or on a weekday; he brings an Asham Taluy:

(Rav): If Shuman and Chelev were in front of him, and he does not know which he ate, he is liable;

If there was one piece and he ate it, he is exempt.

Question: What is his reason?

Answer #1 (Rava): He learns from "v'Asesah Achas mi'Kol Mitzvos Hash-m." He must be Shogeg regarding two Mitzvos.

Answer #2 (R. Zeira): When there were two pieces, we (e.g. an expert) can resolve the doubt (even after he ate), but not if there was only one piece.

Rava and R. Zeira argue about when one piece was a k'Zayis and the other was a half k'Zayis (and he ate the former):

We can resolve the doubt, but there were not two pieces.

18a - Answer #3 (Rav Nachman): Rav obligates when there are two pieces, because the Isur was Nikva. (There definitely was Isur there.) He exempts regarding one piece because the Isur was not Nikva.

The three answers argue about when there were two pieces, and a Nochri ate one, and a Yisrael ate the other;

Rava exempts, for there were not "Mitzvos" when the Yisrael ate;

R. Zeira exempts, for we cannot resolve the doubt;

Rav Nachman obligates, for the Isur was Nikva.

Eruvin 34a (Mishnah): If Yom Tov is before Shabbos, to be Me'arev for both days, he takes the Eruv (to the desired place of Shevisah) on Erev Yom Tov, after dark he takes it home, and the next day he takes it back and stays there until dark.

Question (Rav bar Sheva): (Why must he bring the Eruv?) We should say that Ho'il (since) he could take it with him, it is as if he took it!

Answer (R. Zeira): We decree due to when Yom Tov follows Shabbos. (Ho'il does not apply then, since he may not carry it on Shabbos.)

Rishonim

Rambam (Hilchos Shegagos 8:2): One brings an Asham Taluy only if there was an Isur Kavu'a. If one did a Melachah, and he does not know if it was on Shabbos or on a weekday; or it was on Shabbos but he does not know which Melachah he did, he brings an Asham Taluy.

Lechem Mishneh: The Rambam rules like the opinion that requires two pieces for Asham Taluy so there will be Isur Kavu'a. Tosfos (below) says that Safek Shabbos is an Isur Kavu'a when he did Melachah Bein ha'Shemashos at the end of Shabbos, for the day was Asur. The Rambam connotes that Melachah even Bein ha'Shemashos at the start of Shabbos is called Isur Kavu'a. If he meant like Tosfos, he should have specified.

Tosfos (17b DH mid'Seifa): Regarding Shabbos and a weekday, the case of two pieces is when he did Melachah Bein ha'Shemashos, i.e. at the end of Shabbos. This was an Isur Kavu'a, for the entire day was forbidden. The Isur can be clarified, e.g. if a large amount of Melachah was done and only a small part of the night passed. If so, surely some was during the day.

Aruch l'Ner (on Tosfos, b'Emtza Devarav): The Lechem Mishneh connotes that the Rambam obligates even for a Melachah in the middle of the day, just he is unsure whether it was Shabbos or a weekday. The Toras Kohanim (Vayikra 12) says that he did Melachah Bein ha'Shemashos. This is like Tosfos. Tosfos explains that Isur Kavu'a is like Nischazek Isur (an Isur was established to be there). This is like the Magen Avraham (below). What forced them to say so? Ikva means only that we know that there was Isur. This applies at the beginning of Shabbos, just like at the end! However, the Toras Kohanim mentions 'Shabbos and a weekday.' This connotes that Shabbos was first, like Tosfos says.

Rashi (Shabbos 8b DH v'Rebbi): Rebbi holds that Chachamim decreed Shevus only during Vadai Shabbos, but not Bein ha'Shemashos.

Rashba (Eruvin 32b DH Hachi): When Motza'ei Yom Tov is Shabbos, we decreed not to rely on Ho'il, due to when Motza'ei Shabbos is Yom Tov. We permit an Eruv in a tree (even if the person is more than four Amos away). We do not decree lest he use it for Yom Tov after Shabbos, for also then he can get to it Bein ha'Shemashos. Just like Rebbi permits Shevus Bein ha'Shemashos of Erev Shabbos, he permits Bein ha'Shemashos of Motza'ei Shabbos.

Hagahah in Tosfos (34a DH v'Amai): Rashi holds that if one's Shevisah and Eruv are both on Reshus ha'Rabim, according to Rebbi he need not bring the Eruv near his Shevisah (for there are ways to carry in Reshus ha'Rabim that are only mid'Rabanan). We cannot say that we decree due to Yom Tov after Shabbos (for even then he may carry).

Poskim

Shulchan Aruch (OC 342:1): Anything forbidden mid'Rabanan, Chachamim did not decree about it Bein ha'Shemashos if it is for the sake of a Mitzvah or in pressed circumstances.

Magen Avraham (1): It is not clear whether also on Motza'ei Shabbos Chachamim did not decree. The end of the day is different than the beginning of the day. The Kedushah does not leave due to Safek, like in Siman 386 (below). Also see 562 (below).

R. Yehudah Bachrach (on Tosfos 34a): Seemingly, the Hagahah settles the Magen Avraham's question (Shevus is permitted even on Bein ha'Shemashos of Motza'ei Shabbos). However, perhaps indeed it is forbidden, just we do not decree (for every Shabbos) due to an Isur mid'Rabanan when Yom Tov is after Shabbos. This requires investigation.

Birkei Yosef (2): The Rashba equates Bein ha'Shemashos of Erev Shabbos and Motza'ei Shabbos.

Beis Meir: I say that Chachamim did not decree Shevus Bein ha'Shemashos also on Motza'ei Shabbos. The Gemara says Stam 'Bein ha'Shemashos', which refers also to Motza'ei Shabbos. Rashi explains that Shevus is mid'Rabanan, and Bein ha'Shemashos is a Safek, so we are lenient about a Safek mid'Rabanan. In Sukah, the Rashba (Ritva 46b DH Amar) and Ran (22b DH Amar) say that if one did not take a Lulav on Hoshanah Rabah until Bein ha'Shemashos, he is exempt, for we are lenient about a Safek mid'Rabanan. (After the first day, Lulav is mid'Rabanan.) Even though it is the end of the day (and he was obligated during the day), we are lenient. In Siman 386 we are stringent about Hekdesh and Konam because they are mid'Oraisa, so we are stringent about a Safek about them. At the end of the day, the Isur was Nischazek, so it does not leave due to a Safek. At the start of the day, Heter was Nischazek, so Kedushah does not come due to a Safek. (I later found that Beis Yakov (?) 121 says like this.) The Rashba and Ran are even according to R. Yosi, who is stringent about a Safek mid'Rabanan when there was Chezkas Isur. Regarding fasting, the Beis Yosef says that the custom to wait until Tzeis ha'Kochavim, for we are not experts about when Bein ha'Shemashos is. This is clear from the Rosh and Semak. Rav Chisda himself said that one must fast until the sun sets, which implies that Bein ha'Shemashos is permitted. We say that Tish'ah b'Av is different, for we are more lenient about start of the day. I.e. there is no custom to be stringent about Bein ha'Shemashos at the start of the day. Letter of the law, one may be lenient about laws mid'Rabanan Bein ha'Shemashos at the beginning and end of the day, like the Rashba and Ran. Perhaps Semak said so even if one vowed to fast, and it is mid'Oraisa. However, in practice we must be stringent, for we are not experts about when Bein ha'Shemashos is.

Mishnah Berurah (2): The Magen Avraham was unsure whether Bein ha'Shemashos of Motza'ei Shabbos is more stringent. The Chayei Adam is stringent. The Beis Meir says that letter of the law one may be lenient for the sake of a Mitzvah, but in practice one must be stringent because we are not experts about when is Bein ha'Shemashos.

Bi'ur Halachah (DH Bein): The Beis Meir proved that there is no difference between the start of the day and the end of the day. The Gra and Korban Nesan'el say that letter of the law, we fast until Tzeis ha'Kochavim. We are stringent like R. Yosi (that Bein ha'Shemashos is only a moment before Tzeis ha'Kochavim). According to him, before this is not even Safek night. We do not apply two leniencies, to permit a Safek (Bein ha'Shemashos) and to follow R. Yehudah's opinion about Bein ha'Shemashos (that it is the time to walk three quarters (or two thirds) of a Mil (i.e. about 13 minutes) before Tzeis ha'Kochavim). Also the Rambam connotes that Bein ha'Shemashos of Motza'ei Shabbos is permitted. He forbids Shevus only b'Itzumu (in the essence) of the day. He permits Bein ha'Shemashos if there is a need. However, if we are unsure whether Bein ha'Shemashos began, surely one must be stringent. Lack of knowledge is not called a Safek (Pri Megadim 261). I was unsure (Bi'ur Halachah 261) if we may be lenient to permit Shevus Bein ha'Shemashos, and to say that it starts at Shki'ah, like R. Yehudah. Perhaps on Motza'ei Shabbos we are lenient only for Bein ha'Shemashos of R. Yosi! This requires investigation. Therefore, on Motza'ei Shabbos one should be stringent until close to Tzeis ha'Kochavim, for then surely it is Bein ha'Shemashos of R. Yosi. The Beis Meir holds like this. He did not mention Bein ha'Shemashos of R. Yosi, for it is very very short.

Kaf ha'Chayim (8): Also Yeshu'os Yakov and Chemed Moshe are stringent about Motza'ei Shabbos. Tosefes Shabbos says that it is clear from Tosfos 34a and Rashi Shabbos 8b that we are lenient about Bein ha'Shemashos also on Motza'ei Shabbos. Nesiv Chayim says that the Mishnah says 'Safek dark, Safek not dark' to teach that Motza'ei Shabbos is included. The Birkei Yosef and most Poskim are lenient. Therefore, on Bein ha'Shemashos of Motza'ei Shabbos one may tell a Nochri to light a lamp for the sake of a Mitzvah, e.g. Seudah Shelishis or prayer.

Shulchan Aruch (386:9): If one said (on Erev Shabbos) 'today this loaf is Chulin, and tomorrow it is Kodesh or Konam (forbidden like Hekdesh)', one may use it for an Eruv, for Bein ha'Shemashos it was not Vadai Kodesh, and it was permitted during the day. If one said 'today it is Konam, and tomorrow it is Chulin', one may not use it for an Eruv, for it is forbidden until dark.

Magen Avraham (12,13): In the first case, Kedushah does not come on it (Bein ha'Shemashos) amidst Safek. In the latter case, the Kedushah does not leave amidst Safek.

Shulchan Aruch (562:1): Any fast that one does not complete until Tzeis ha'Kochavim is not a fast, and he may not say 'Aneinu' in Shemoneh Esre.

Gra (DH Ad): The Rosh and Mordechai say so, but the Gemara brings an argument about whether Bein ha'Shemashos of Tish'ah b'Av is forbidden. This implies that Bein ha'Shemashos of other fasts is surely permitted. However, the Mordechai (Ta'anis 975, citing R. Elchanan) says that one must fast until Tzeis ha'Kochavim. There is an argument about (the start of) Tish'ah b'Av, for the start of the day is more lenient than the end of the day. Also Hagahos Maimoniyos says so. However, R. Yonah and the Rosh (Shabbos 2:23) permit Bein ha'Shemashos of an individual's fast, even at the end of the day. The Gemara connotes like this, for it says 'its Safek is permitted.'

Rema: The custom is to say Aneinu even though we do not complete the fast until Tzeis ha'Kochavim.