(Mishnah): If two merchants entered a city, and one said, 'My produce is untithed, my friend's is tithed', he is not believed;

R. Yehudah says, he is believed.

Question: If he said 'I and my friend are Kohanim', R. Yehudah says that he is not believed (to feed his friend Terumah)!

Answer (Abaye): R. Yehudah is lenient about Demai because most Amei ha'Aretz do tithe.

56b (Abaye): R. Yehudah holds that Chachamim strengthened their enactment regarding Kesuvah (a verbal stipulation that she received part of it is not sufficient) more than regarding Torah laws.

Question: R. Yehudah holds that Chachamim did not strengthen their enactment of Demai (to suspect that merchants scheme to lie for each other)!

Mishnah: If two merchants entered a city, and one said, 'My produce is new, my friend's is old. Mine is untithed, my friend's is tithed', they are not believed;

R. Yehudah says, they are believed.

Answer #1 (Abaye): A Vadai Rabbinical enactment was strengthened, but not one that is based on Safek.

Answer #2 (Rava): Chachamim were lenient about Demai (because most Amei ha'Aretz tithe).

Shabbos 23a: We bless '...Asher Kidshanu b'Mitzvosav v'Tzivanu Lehadlik Ner Shel Chanukah', even though it is mid'Rabanan.

Question (Rav Amram - Mishnah): One may tithe Demai when naked.

It says "V'Hayah Machanecha Kadosh" (one may not say a Berachah or any Divrei Kedushah where Ervah is visible)!

Answer #1 (Abaye): We bless on all Vadai Mitzvos mid'Rabanan, but not on tithing Demai, for it is a Safek (perhaps it was already tithed).

Question: In Chutz la'Aretz, people observe a second day of Yom Tov due to Safek, yet they bless on it (e.g. Kidush)!

Answer: (According to letter of the law, they should not bless.) Chachamim were concerned that if they will not bless, they will treat it lightly.

Answer #2 (Rava): Most Amei ha'Aretz tithe (Demai is not really a Safek. It is a mere stringency mid'Rabanan to tithe it.

Berachos 21a (Rav Yehudah): If one is unsure whether or not he said Keri'as Shema, he need not say it due to Safek. If one is unsure whether or not he said Emes v'Yatziv, he must say it.

(He holds that) Keri'as Shema is mid'Rabanan, and Emes v'Yatziv is mid'Oraisa.

33a (Rav): Anyone who says an unnecessary Berachah transgresses "Lo Sisa (Es Shem Hash-m Elokecha la'Shav, saying Hash-m's name in vain.)"

Rishonim

Rif and Rosh (Sukah 4:5): We sit in the Sukah on Shemini Atzeres but do not bless, for this is a contradiction to Yom Tov.

Rambam (Hilchos Sukah 6:13): We sit in the Sukah on Shemini Atzeres but we do not bless 'Leshev ba'Sukah'. Similarly, a Tumtum or Androginus never blesses on the Sukah because it is a Safek whether 'he' is obligated.

Rebuttal (Ra'avad): Rava says that we do not bless on tithing Demai because most Amei ha'Aretz tithe (and the Halachah follows him). This implies that we would bless on a Safek mid'Oraisa.

Defense (Magid Mishnah): Abaye (Shabbos 23a) says that we do not bless on tithing Demai because it is a Safek. Rava agrees that we do not bless on a Safek; he merely teaches that Demai is not considered a Safek.

Lechem Mishneh: The Ra'avad says that we do not bless on the eighth day because this is a contradiction to Yom Tov, like the Rif says. Most say that the Rif holds like the Rambam, that we do not bless on a Safek. He says that we do not bless due to the contradiction because one might have thought that one should bless lest people disgrace the day, like the Gemara says regarding Yom Tov Sheni.

Kesef Mishneh (Milah 3:6): We bless only where Chachamim enacted to bless. We do not bless mi'Safek, even regarding Mitzvos mid'Oraisa!

Rambam (Hilchos Kri'as Shma 2:13): If one is unsure whether or not he said Keri'as Shema, he reads it and blesses before and after. If one knows that he said Keri'as Shma but is unsure whether or not he blessed before and after, he does not bless again.

Rosh (Berachos 3:15): The She'altos learns from Berachos 21a (that one must say Emes v'Yatziv mi'Safek because it is mid'Oraisa) that since all Berachos are mid'Rabanan, one does not repeat them if he is unsure whether or not he said them.

Rosh (Chulin 6:1): R. Yonah says that one must bless on Kisuy ha'Dam of a Koy, for it is a Safek mid'Oraisa (whether or not Kisuy is required, for perhaps it is a Chayah). The Gemara (Shabbos 23a) says that we do not bless on Demai because it is a Safek mid'Rabanan. This is not a proof. The Gemara teaches why Demai is different than other enactments on which we bless. We do not bless on a Safek, lest we transgress Lo Sisa.

Tosfos (Kesuvos 24a DH Abaye): Even though Abaye says that we do not bless on tithing Demai because it is a Safek (Shabbos 23a), and that Chachamim did not strengthen their enactment of Demai (to suspect that merchants scheme to lie for each other - Kesuvos 56b), he agrees that most Amei ha'Aretz tithe.

Poskim

Shulchan Aruch (OC 67:1): If one is unsure whether or not he said Keri'as Shema, he reads it and blesses before and after. If one knows that he said Keri'as Shma but is unsure whether or not he blessed before and after, he does not bless again.

Beis Yosef (DH Safek): We hold that Kri'as Shma is mid'Oraisa. The Rambam and R. Yonah say that one blesses on a Safek Mitzvah mid'Oraisa. Some disagree.

Beis Yosef (DH u'Mah): The She'altos holds that since Berachos are mid'Rabanan, one need not repeat them mi'Safek. R. Mano'ach (Kri'as Shma 2:13) forbids to bless mi'Safek, for we are stringent about Lo Sisa.

Kaf ha'Chayim (3): The Pri Chodosh infers that the She'altos holds that one transgresses Lo Sisa mid'Oraisa for a Berachah l'Vatalah. The Rivash and Terumas ha'Deshen proved that it is only mid'Rabanan; the Drashah is an Asmachta. The Rof says that we are lenient about Safek Berachos. However, the Levush says that he transgresses mid'Oraisa.

Taz (1): Tosfos explains that Rav Yehudah requires repeating Emes v'Yatziv mi'Safek when one did not mention Yetzi'as Mitzrayim, i.e. perhaps he also omitted Parshas Tzitzis in Keri'as Shema. If he said all of Shma, Emes v'Yatziv is mid'Rabanan.

Mishnah Berurah (1): Regarding other Mitzvos mid'Oraisa that one must do due to Safek, e.g. a Tumtum must put Tzitzis on his garment, we do not bless because the Berachah is mid'Rabanan and we are lenient a Safek. However, some Poskim say that whenever the person was definitely obligated and is unsure whether or not he was Yotzei, e.g. Lulav or Shofar on Yom Tov Rishon, he repeats the Mitzvah and blesses, just like Kri'as Shma. However, many exempt even in this case. Surely if it is Bein ha'Shemashos he does not bless, for perhaps he is not obligated in the Mitzvah at all now.

Mishnah Berurah (3): Seemingly, if the time for Shma (three hours) passed, he would not bless, for then there is no Mitzvah mid'Oraisa. However, there is a Mitzvah mid'Oraisa to mention Yetzi'as Miztrayim. The enactment of Emes v'Yatziv is until four hours. One should say a verse of Yetzi'as Miztrayim to be Yotzei the Safek. The Gemara clearly says that one must mention Yetzi'as Miztrayim at night. The Pri Megadim is unsure whether or not this is mid'Oraisa. If it is, one who is unsure whether or not he said it must repeat it. The Sha'agas Aryeh says that it is mid'Oraisa. One who read Shma Bein ha'Shemashos was not Yotzei, for it is Safek day, so he must be stringent.

Mishnah Berurah (4): Some say that only the first Parashah or verse of Shma is mid'Oraisa. Chachamim enacted to say all of Shma with the Berachos, except in certain cases. If one may eat knows that he read what is mid'Oraisa, he need not repeat Shma due to a Safek about the rest. However, the Shulchan Aruch (64:3) is stringent about one who is unsure whether he is in the middle of the first or second Parashah. This was part of the enactment.

Shulchan Aruch (204:3): If one is unsure about any Berachah he does not bless before or after, except for Birkas ha'Mazon, which is mid'Oraisa.

Mishnah Berurah (47:1): Most hold that Birkas ha'Torah is mid'Oraisa, so one must say it mi'Safek. One says only the Berachah 'Asher Bochar Banu'. It is best if he can hear the Berachah from someone else, or intend to be Yotzei through Ahavah Rabah and learn immediately after Tefilah.