Gemara

Question: A Safek is Motzi mi'Ydei Vadai (permits what was definitely forbidden)

(Beraisa): If a Chaver (one trustworthy about tithing) died and left Peros, even if they were harvested that day, we assume that he tithed them.

Even though they were definitely Tevel, and we are in doubt whether he tithed them, we permit them!

Answer #1: There, he definitely tithed them, like R. Chanina Chuza'ah taught.

(R. Chanina Chuza'ah): There is a Chazakah that anything one gets from a Chaver was tithed.

Answer #2: The Peros were not definitely forbidden. Perhaps he did like R. Oshaya's scheme;

(R. Oshaya): One may scheme, and bring Peros into his house with the chaff, and his animal may eat without tithing.

Question (Beraisa - R. Yehudah): A case occurred in which a slave dropped a miscarriage into a pit. A Kohen stood over it to see its gender. Chachamim ruled that he is Tahor, because weasels are often in pits. Perhaps they dragged the miscarriage away and he was not over it.

There definitely was a miscarriage in the pit, and we are unsure if it was dragged away, and we assume that it was!

Answer #1: A fetal sac was in the pit. (Perhaps it was not Tamei.)

Answer #2: Since weasels are in the pit, certainly they dragged it away.

Berachos 20a (Mishnah): Women are obligated in Birkas ha'Mazon.

Question: This is obvious! It is a Mitzvas Aseh she'Lav ha'Zman Gerama (it applies at all times).

Answer: One might have thought that it is like Zeman Gerama, for it says, "b'Tes Hash-m... v'Lechem ba'Boker Lisbo'a".

Question (Ravina): Is her obligation mid'Oraisa or mid'Rabanan?

Answer (Rava - Beraisa): A tradition from Sinai teaches that a son may bless for (and exempt) his father, and a wife may bless for her husband.

If she were obligated only mid'Rabanan, she could not exempt a man!

Objection: Surely, a minor is exempt mid'Oraisa, yet it also says that a son can bless for his father!

Answer: The man's obligation to say Birkas ha'Mazon was only mid'Rabanan (he did not eat to satiation).

Rishonim

Rif (Berachos 11b): Women are obligated in Birkas ha'Mazon, for it is a Mitzvas Aseh she'Lav ha'Zman Gerama.

R. Yonah (DH Gemara): They are obligated mid'Rabanan.

Rambam (Hilchos Berachos 5:1): Birkas ha'Mazon is obligatory for women. It is a Safek whether this is mid'Oraisa.

Rosh (Berachos 3:13): The question was not settled.

Poskim

Shulchan Aruch (OC 186:1): Birkas ha'Mazon is obligatory for women. It is a Safek if this is mid'Oraisa and they can be Motzi a man, or if it is only mid'Rabanan and they can be Motzi only one obligated only mid'Rabanan.

Beis Yosef (DH v'Chasav): The Rashba says that the Halachah does not follow Ravina. Rather, we hold like Rava who obligates women mid'Oraisa. Firstly, Rava was Ravina's Rebbi. Also, the Gemara said that obviously, women are obligated. The Ra'avad agrees.

Sha'ar Efrayim (11): If a woman ate and is unsure whether or not she blessed, we cannot exempt her due to Sefek Sefekah, i.e. perhaps she blessed, and even if she did not perhaps she is exempt mid'Oraisa. This is wrong. On the side that she did not bless, she surely did not bless, and mid'Rabanan she must bless!

Birkei Yosef (4): It is a Sefek Sefekah whether she is obligated now mid'Oraisa, so she is exempt from her mid'Oraisa obligation. It is a Safek whether she is obligated mid'Rabanan, are we are lenient about a Safek mid'Rabanan, so she does not bless! At first I wanted to say that this depends on whether Safek Motzi mi'Ydei Vadai. The Gemara asked from a Beraisa, and gave two answers. Rashi explains the second answer that perhaps he did like R. Oshaya's scheme, and brought Peros into his house with the chaff for his animals to eat. Had he entered them for human consumption, they would be obligated mid'Rabanan. We would rely on the Chazakah of a Chaver for the Isur mid'Rabanan. Rashi connotes that we permit only due to the Chazakah of a Chaver, even though there is a Sefek Sefekah regarding the Chiyuv mid'Oraisa and a Safek regarding the Chiyuv mid'Rabanan, just like a woman who is unsure if she blessed. The same applies to one answer of the Ri, that we discuss Peros that only animals eat, for human food would be obligated mid'Rabanan. Really, there is no proof from Rashi. The Rashba (361) holds that when one brought Peros into his house with the chaff, even people may eat Keva (without tithing). He asked, if so what does Chezkas Chaver help for? Anyone's Peros are exempt due to Sefek Sefekah! He answers that the Safek that they are not tithed is better than the Safek that one did like R. Oshaya. We leave the Peros on their Chazakah that they were not tithed. This weakens the side that they are tithed. For a Chaver, there is a Chazakah that he tithed them. Alternatively, a Chaver's Peros are assumed to be tithed, and an Am ha'Aretz's are assumed to be Vadai untithed. This can explain why Rashi needed to say that the Peros were entered for animals to eat (since he obligates for human consumption). We would not be lenient about the Safek mid'Rabanan, due to the Chazakah that the Peros are Tevel. We permit only due to the Chazakah of a Chaver. However, according to one answer of the Ri, a Safek mid'Rabanan is Motzi mi'Ydei Vadai. We permit the Peros only for animals, but a person must tithe before eating them. If so, my proof above is valid. However, one can reject this. The Rambam and Shulchan Aruch say that one does not say any Berachah mid'Rabanan due to Safek. Any Berachah not on food, e.g. Tefilah, is not considered a Vadai (obligation), so he does not bless. If one ate, this is (a Vadai obligation) like Peros Tevel. Ein Safek Motzi mi'Ydei Vadai! The Mishneh l'Melech (Hilchos Chametz 2:1) says that if we are unsure if Chametz was eaten, even though after Bitul it is a Safek mid'Rabanan, Ein Safek Motzi mi'Ydei Vadai, and Bedikah is needed. However, one answer in Tosfos obligates Bedikah only if he did not do Bitul. Why is the Tur lenient about Berachos on food, and also about a Safek whether one washed his hands (OC 160)? I say that the Tur holds that Safek Motzi mi'Ydei Vadai for mid'Rabanan laws, but we are more stringent about Chametz, because the Torah was more stringent about it, or because Bedikah was enacted for Safek (Magid Mishneh citing the Ro'oh).

Birkei Yosef: If one surely owed, and it is a Safek if he returned, he is liable. However, perhaps monetary laws are different. Perhaps we do not say Ein Safek Motzi mi'Ydei Vadai when there is concern for a Berachah Levatalah. One can say so even according to the opinion that Berachah Levatalah is only mid'Rabanan.

Mishnah Berurah (3): The Sha'ar Efrayim, Chayei Adam and Magen Giborim obligate her. R. Akiva Eiger and the Birkei Yosef exempt her, and the Pri Megadim leans to agree. We do not protest against one who relies on the first opinion to bless again.

Bi'ur Halachah (DH Ela): Even though the Shulchan Aruch rules that it is a Safek if she is obligated mid'Oraisa, the Rif, Rav Hai Gaon, Ramban, Rashba, Ritva, and Ran obligate her mid'Oraisa. One may rely on them and the Sha'ar Efrayim and Acharonim who say to bless due to Safek.

Kaf ha'Chayim (184:25): Most Poskim say that she does not bless. We follow them, for Safek Berachos Lehakel. If possible, she should eat more and bless, or hear Birkas ha'Mazon from someone else.

Yechaveh Da'as (6:10): She should not say Birkas ha'Mazon due to Safek, but it is good to think Birkas ha'Mazon in her heart, since the Rambam and Semag say that she is Yotzei through this. Berachah Levatalah applies only to one who says the words. A man who ate to satiation must bless due to Safek and say the words.