Answer #1: According to R. Yehoshua, we need "she is To'evah, but her children are not To'evah" lest we say that her (Machazir Gerushaso's) children are To'evah because Tum'ah is written regarding her, like it says about Arayos.

Even according to R. Yosi ben Kiper, who establishes [the Tum'ah written regarding Machazir Gerushaso] to discuss a Sotah, we say that the verse does not leave its simple meaning.

Even according to the opinion that once it was uprooted, it is totally uprooted, we need "she is To'evah" lest we say that it applies also to Machazir Gerushaso.

Answer #2: We need "Hi" to exclude, lest we expound from "To'evah" that her children are To'evah.

Question: Below, they asked R. Yehoshua about Bnei Tzaros of Beis Hillel according to Beis Shamai. We say that this was in order to resolve the law of the child of Machazir Gerushaso;

How can we learn from there? Perhaps we disqualify the child of Machazir Gerushaso because Tum'ah is written about her, or due to "To'evah"!

Alternatively, even if the child of Yevamah l'Shuk is Pasul, perhaps the child of Machazir Gerushaso is Kosher, for "she is To'evah, but her children are not To'evah"!

We can say that this comes to distinguish, that children of Yevamah l'Shuk are To'evah!

Answer: They did not think of these Drashos. They asked only whether or not we make a Kal va'Chomer regarding a Yevamah l'Shuk.

Explanation (Yerushalmi): He separated Ma'aser Sheni and redeemed it, and apportioned the Ma'aser Aniyim, and consumed the [redemption] money in Yerushalayim.

Observation: We could have asked 'according to you, how could he adopt the stringencies of both? It says "a fool walks in darkness"!'"

The Gemara asks this in Eruvin (7a) and Rosh Hashanah (14b).

Inference: The opinion that they did not do like their teachings says so even when Beis Shamai are stringent, [in practice] they were lenient like Beis Hillel.

Question: A Mishnah (Taharos 9,8, brought in Gitin 16a) says that Nitzuk u'Ketafres (a liquid poured through the air or flowing down an incline), or a liquid Tofe'ach (it wets what touches it), are not connections for Tum'ah or Taharah, but Tofe'ach Lehatfi'ach (it wets what touches it, enough to wet something else) connects. (Here we require an opening k'Shfoferes ha'Nod!)

Answer #1 (R. Tam): The opening must be k'Shfoferes ha'Nod, but it suffices that the water that goes through it is Tofe'ach Lehatfi'ach.

Objection (Ri - Mishnah (Mikva'os 6:9)): If the wall between two Mikva'os was cracked vertically, they join. If it was cracked horizontally, it joins only if in one place there is an opening k'Shfoferes ha'Nod;

Citation (cont.): R. Yehudah says oppositely;

Citation (cont.): If there was a breach for a height like [the thickness of] a garlic peel and the width ki'Shfoferes ha'Nod [they join].

Inference: On top where nothing separates [the Mikva'os], the water must "float" [above wall] for the height of [the thickness of] a garlic peel and the width of Shefoferes ha'Nod. Tofe'ach Lehatfi'ach does not suffice;

When there is a hole between them, and the wall separates, it seems that we require water ki'Shfoferes [ha'Nod].

Also, if the water coming through the hole is only Tofe'ach Lehatfi'ach, there is not water the width of ki'Shfoferes ha'Nod, for the hole is not round, rather, square. We say that it is like [the width of] two fingers [rotating and] returning to their place.

Conclusion: Rather, the hole must be full. When the water floats above, [the thickness of a garlic peel and the width of ki'Shfoferes ha'Nod suffices.

Answer #2 (Ri): Nitzuk u'Ketafres (a poured or flowing liquid) in the Mishnah do not refer to connecting Mikva'os. Rather, they refer to Hashakah (connecting water to a Mikveh);

If there is Tamei water, and he connects it to a river and joins them through Nitzuk, Ketafres or a liquid Tofe'ach, this is not a connection. Tofe'ach Lehatfi'ach is a connection.

Support #1: Based on this, Taharah resembles Tum'ah. This was explicitly taught regarding Hashakah in Taharos 8:9;

Support #2: In Gitin 16a, we conclude "perhaps this refers to Mikva'os, and it is R. Yehudah". This implies that before this, we did not establish it regarding Mikva'os;

Also now that we establish it regarding Mikva'os, it is only like R. Yehudah, but Rabanan hold that Tofe'ach Lehatfi'ach is not a connection.

Also according to R. Yehudah, Tofe'ach Lehatfi'ach is a connection only due to Gud Achis (we project downward), like the case of [one who immersed in a Mikveh of exactly 40 Sa'im, and a second person immersed while the first is leaving, and] his feet touch the water, which R. Yehudah discusses. (We consider all the water on his body to be connected to the Mikveh, so it still has a Shi'ur.)

However, when Gud Achis does not apply, e.g. level ground, Tofe'ach Lehatfi'ach is not a connection. We require water floating the thickness of a garlic peel.

It seems that also the case when they were breached to each other for height of a garlic peel is like R. Yehudah, who was mentioned there in the Reisha.

Reference: What is difficult with this we explained in Gitin. This is not the place to elaborate.

Inference: Rashi connotes that R. Yochanan suspected that R. Tzadok was not concerned for an Am ha'Aretz touching [the olives].

Implied question: R. Tzadok was a Kohen, and garments [even] of Perushim (pious people who go beyond the letter of the law) are Medras (considered Tamei) for those who eat Terumah. (All the more so, he must be concerned for Amei ha'Aretz! Why did R. Yochanan suspect him?)

Answer #1: He suspected him because R. Tzadok was a Talmid of Beis Shamai. Perhaps he was not careful to guard [the olives] in Taharah because Beis Shamai hold that one need not puncture the Kli [in which he harvests them].

Answer #2 (Ri): Surely, R. Yochanan knew that R. Tzadok bought the barrel from an Am ha'Aretz.

Rashi's opinion: Mohel of (juice that comes from) olives is Machshir.

Support (Machshirin 6:5 - Mishnah): Whey is like milk. Mohel of olives is like [olive] oil.

Question: In Shabbos (17a), Rabbeinu Yosef explained that they did not decree to harvest olives in Taharah because the reason for grapes (to harvest them b'Taharah) does not apply;

We are concerned lest one harvest grapes in plastered boxes [to hold the juice that exudes. It is Machshir.] This does not apply to harvesting olives, for Mohel is not Machshir!

Answer: There are three kinds of Mohel. All agree that Mohel that comes through harvesting is not Machshir;

What comes through Itzetza, i.e. they become warmed in the Komer (a Kli) and Mohel comes out, R. Yakov and R. Shimon argue about this. R. Shimon is Metaher (it is not Machshir), and R. Yakov is Metamei.

Here we discuss a barrel that must be punctured. We must say that it (Mohel) is considered like what comes out through Ikul Beis ha'Bad (a basket in which olives are pressed);

R. Shimon agrees about it, for if not Beis Hillel would be difficult for him.

Question: Why does it mention the child of Machazir Gerushaso? He should have resolved the child of an absolute Yevamah l'Shuk according to Beis Hillel, which we were discussing!

Answer: It is because another time, they asked R. Yehoshua about her;

Citation (Nidah 69) Question (people of Alexandria): May the daughter of Meshulachas (Machazir Gerushaso) marry a Kohen? Do we say a Kal va'Chomer...

Question: We should learn this, that a divorcee becomes profaned, from a Kal va'Chomer from a widow!

Answer (Rashi): She is not disqualified from Terumah of her father's house, like we say below (69a) that a Bi'ah of Chayavei Lavin disqualifies only if he was forbidden to her from birth;

This excludes Machazir Gerushaso and Yevamah l'Shuk. He was not forbidden to her from birth.

Question #1: Granted, we can learn from "Ki Sihyeh l'Ish Zar" only one who was forbidden to her from birth. However, we should learn from a Kal va'Chomer that she becomes profaned!

Question #2 - Citation (below 44b) Question: How can we learn Chayavei Kerisos from a widow to a Kohen Gadol? A widow is different [for she becomes profaned]!

Citation (cont.) Answer: Also here, through Bi'ah he made her a Zonah!

Summation of question: Why do we need that he made her a Zonah? We should learn this itself from the Kal va'Chomer, that she becomes profaned!

Question #3: Below (68a), with difficulty we expound that an Amoni, Mo'avi, Mitzri and Edomi all disqualify through Bi'ah.

We should know this from the Kal va'Chomer!

Answer (to all three questions): We cannot learn from the Kal va'Chomer that she becomes profaned, for Chilul is only through Isurei Kehunah;

We say in Kidushin (77b) that this is why one who has Bi'ah with his sister makes her a Zonah, but not a Chalalah.

Implied question: Below, we learn that she becomes profaned through Bi'ah of a convert from Amon, Mo'av, Mitzrayim or Edom, or a Nochri, Chalal, Nasin or Mamzer, even though these are not Isurei Kehunah!

Answer: There, we expound a verse. However, we could not learn from a Kal va'Chomer;

This is why Chalalah is extra (the Torah did not need to write the Isur of a Chalalah to a Kohen Gadol, for she is forbidden to all Kohanim - Kidushin 77b), to teach that we do not learn from the Kal va'Chomer.

Distinction: Regarding her son, surely we would have learned from the Kal va'Chomer. However, to disqualify her, to make her a Chalalah, i.e. she was Kosher and became profaned, we would not learn.

Question: We should learn from a Tzad ha'Shavah of a widow and a Nochri or slave, or a widow and a Mitzri or Edomi!

In Kidushin (78a), it is clear that we learn from a Tzad ha'Shavah from Isurei Kehunah. R. Yehudah learns that a convert disqualifies through Bi'ah, from [a Tzad ha'Shavah of] a Chalal and Mitzri...

Answer: We can say that only R. Yehudah holds that we learn from a Tzad ha'Shavah from Isurei Kehunah, but Rabanan disagree. They hold that the daughter of a male convert is unlike the daughter of a male Chalal.

Question: Why does R. Yehudah need a verse to teach that converts of Amon, Mo'av... disqualify through Bi'ah? He should learn from a Tzad ha'Shavah, from either a widow [to a Kohen Gadol] or Chalal, and a Nochri and slave.

When you ask "you cannot learn from a Chalal, for this is an Isur Kehunah", Nochri and slave Yochichu (prove that it does not depend on this).

[When you ask that] you cannot learn from a Nochri and slave, for Kidushin does not take effect with them, Chalal Yochi'ach.

Answer: R. Yehudah holds like R. Akiva, and holds that a Mamzer results from a Nochri and slave. Therefore, we cannot learn from a Nochri and slave, for there [the child] is a Mamzer.