1) THE VIEW OF RABAN GAMLIEL THAT THE WOMAN IS BELIEVED
QUESTION: Raban Gamliel teaches in two different cases (in the Mishnah on 12b and in the Mishnah here) that "Bari v'Shema, Bari Adif" -- when two people make claims against each other, and one person is doubtful ("Shema") about his claim and the other is certain ("Bari") about his, the one with the certain claim prevails. Rebbi Yochanan explains why Raban Gamliel needs to teach this law in two different Mishnayos. In the case of the second Mishnah, where the man claims that his wife had relations with another man before they were married and his wife claims that she is a Mukas Etz, Raban Gamliel teaches that the woman is believed to say she is a Mukas Etz even though she has no Migu. In the previous Mishnah, however, where the man claims that his wife had relations with another man before they were married and she claims that she was raped after they were married, it is obvious (according to Raban Gamliel) that she is believed because she has a Migu that she could have said that she was a Mukas Etz.
Why does Rebbi Yochanan mention that the only Chidush of the second Mishnah is that she is believed even though there is no Migu? The Gemara (12b) gives two reasons for why Raban Gamliel says that the woman is believed in the case of the Mishnah there: the first is that she has a Migu (that she could have said she was a Mukas Etz), and the second is that she has a Chazakah (that she was a Besulah). In the second Mishnah, not only is there no Migu, there is also no Chazakah! Why, then, does Rebbi Yochanan not say that the second Mishnah is needed to teach that Raban Gamliel accepts the claim of the woman even when there is no Migu and no Chazakah?
ANSWERS:
(a) The RAN explains that in the case of the second Mishnah, there is a Chazakah. The Chazakah is that Jewish women do not commit Z'nus, and thus Beis Din may assume that she was a Mukas Etz and did not have relations with another man.
This also seems to be the intention of TOSFOS (12b, DH Ela) who implies that there is a Chazakah in the case of the Mishnah here.
(b) RASHI (12b, DH Ukma a'Chazakah) implies that there is no Chazakah in this Mishnah. (When Rashi there explains what the Migu is, he explains what the Migu is in both cases. When Rashi there explains what the Chazakah is, he explains the Chazakah only in the case of the first Mishnah.) When Rebbi Yochanan says that the Mishnah teaches that she is believed ("Bari v'Shema, Bari Adif") without a Migu, he also means to say that she is believed without a Chazakah.

13b----------------------------------------13b

2) BELIEVING A WOMAN IN A CASE WHERE "ROV PESULIM ETZLAH"
QUESTIONS: Raban Gamliel and Rebbi Yehoshua argue in a case where a woman secluded herself with another man and it is not known whether he was Pasul (that is, his Be'ilah invalidates her from marrying a Kohen) or not. She claims that he was not Pasul . Raban Gamliel says that she is believed and she is not Pesulah l'Kehunah, while Rebbi Yehoshua says that she is not believed and there is a concern that she had relations with a Nasin or a Mamzer and thus she may not marry a Kohen.
A Beraisa expands on the Machlokes and says that Rebbi Yehoshua proves that she should not be believed, and thus is Pesulah l'Kehunah, from the case of a Shevuyah (captive) who is not believed to say that she was not defiled by her captors. Rebbi Yehoshua says that the case of a Shevuyah demonstrates that although the woman says that she is Tehorah, it is assumed that she was defiled by her captors. Similarly, the woman should not be believed in the case of the Mishnah here. Raban Gamliel admits that the case of Shevuyah is a valid proof for a case in which the woman is pregnant, in which case it is obvious that she had relations and thus she is not believed to say that she had relations with a man who does not invalidate her to Kehunah, since she has no Migu that she could have said that she did not have relations. In such a case, Raban Gamliel agrees that she is not believed to say that the child is not Pasul. However, in a case in which she is not pregnant, Raban Gamliel contends that no proof may be adduced from the case of Shevuyah because that case is different; there, she was captured by Ovdei Kochavim who are steeped in licentiousness, and thus Beis Din must assume that she was defiled. In contrast, in the case of the Mishnah here -- which is not discussing Ovdei Kochavim -- she was not necessarily defiled. Rebbi Yehoshua replies that even in the case here where there are no Ovdei Kochavim, there was no one watching to make sure that Z'nus did not occur ("Ein Apotropos l'Arayos"), and thus Beis Din must suspect that she willfully had relations with the man with whom she secluded herself.
The Gemara questions ("v'Teipuk Lei...") this interchange between Rebbi Yehoshua and Raban Gamliel: "Why did he not say that there (in the case of Shevuyah), most of the men around her are Pesulim (Rov Pesulim Etzlah)," and that is why Beis Din must assume that she was defiled, "while here (in the case of the Mishnah in which she secluded herself with an unidentified man), most of the men around her are Kesherim (Rov Kesherim Etzlah)," for she is in a Jewish city where most of the men in the city will not invalidate her to Kehunah. These are the words of the Gemara's question.
The Gemara answers that the Beraisa is support for the assertion of Rebbi Yehoshua ben Levi, because it does not differentiate between cases of "Rov Pesulim Etzlah" and "Rov Kesherim Etzlah." Rebbi Yehoshua ben Levi asserts that Raban Gamliel believes the woman and permits her even where "Rov Pesulim Etzlah," while Rebbi Yehoshua does not believe her and prohibits her even where "Rov Kesherim Etzlah."
RASHI explains that the Gemara is asking a question on Rebbi Yehoshua: why does Rebbi Yehoshua say that in a case of "Rov Kesherim" that "Ein Apotropos l'Arayos" and that is why Beis Din suspects her of Z'nus and rules that she is Pesulah? Beis Din should believe her and permit her to a Kohen, since most of the people around her are Kesherim ("Rov Kesherim Etzlah")! Accordingly, Rashi understands that the question of the Gemara is a question on Rebbi Yehoshua's opinion.
Rashi's words are very difficult to understand for a number of reasons.
(a) The TOSFOS HA'ROSH points out that this is not how the words "v'Teipuk Lei" are normally used. Those words normally mean that instead of using one line of reasoning to arrive at this conclusion, the Beraisa should have used another line of reasoning to arrive at the same conclusion. Rashi, though, interprets those words as a direct challenge on the view of Rebbi Yehoshua: instead of saying that the woman is Pesulah, he should use this logic (of "Rov Kesherim Etzlah") to say that she is permitted to a Kohen.
Why does Rashi not explain the question of "v'Teipuk Lei" like the Tosfos ha'Rosh, which is the straightforward understanding of the Gemara? The Tosfos ha'Rosh explains that "v'Teipuk Lei" means that Raban Gamliel does not need to answer Rebbi Yehoshua's question by saying that Ovdei Kochavim are immersed in licentiousness, for he could answer simply that in the case of Shevuyah most of the men around her are Pesulim ("Rov Pesulim Etzlah"), while in the case of the Mishnah most of the men are Kesherim ("Rov Kesherim Etzlah")!
(b) According to Rashi's explanation, the Gemara should have asked another basic question. In the Beraisa, Raban Gamliel agrees with Rebbi Yehoshua in the case of a woman who secluded herself with a man, and now she is pregnant. Why does he concede to Rebbi Yehoshua in the case of a pregnant woman? Raban Gamliel should concede only in a case in which the woman is pregnant and "Rov Pesulim Etzlah," but in the case of a pregnant woman where "Rov Kesherim Etzlah" there is no proof from Shevuyah that she is not believed!
(c) What is Rebbi Yehoshua's proof to argue with Raban Gamliel in a case of "Rov Kesherim"? His proof is only from a case of Shevuyah, where there are "Rov Pesulim Etzlah"! How does Rebbi Yehoshua know that the woman is not believed even in a case where there are "Rov Kesherim Etzlah"? (SHITAH MEKUBETZES)
(d) According to Rashi, the Gemara proves that Raban Gamliel and Rebbi Yehoshua argue even in a case of "Rov Kesherim" and not just in a case of "Rov Pesulim," since Rebbi Yehoshua does not say that he agrees that she is believed in a case of "Rov Kesherim."
Why would we have thought that Rebbi Yehoshua agrees in a case of "Rov Kesherim"? The Mishnah is discussing a case of "Rov Kesherim," and yet Rebbi Yehoshua clearly states that she is not believed and she is Pesulah to Kehunah! It is clear that the Mishnah is discussing a case of "Rov Kesherim" because Rebbi Yehoshua is quoted as prohibiting her because of a fear that she had relations with a Nasin or a Mamzer. If the Mishnah's case is one of "Rov Pesulim," Rebbi Yehoshua would have said that we fear she had relations with a Nochri, and not with a Nasin or a Mamzer who certainly are a minority. (It must be that a Nasin and Mamzer are the minority, and the Mishnah cannot be referring to a case in which most men around her are Nesinim and Mamzerim, because when Rebbi Yehoshua says that "Ein Apotropos l'Arayos," how do we know that he applies it even in a case of "Rov Kesherim"? Perhaps he applies it only in a case where "Rov Pesulim" (such as where most men are Nesinim and Mamzerim), where they are not Ovdei Kochavim (for if there were Ovdei Kochavim, he would not have to say "Ein Apotropos..." because even Raban Gamliel agrees that Ovdei Kochavim are steeped in licentiousness). It must be that the only type of man who is Pasul (who is considered to create a "Rov Pesulim") is a Nochri, who creates a Rov of Ovdei Kochavim. Thus, since Rebbi Yehoshua says "Ein Apotropos l'Arayos" in a case in which there are no Ovdei Kochavim, it must be that it applies in a case where "Rov Kesherim.")