1)

(a)Rebbi Akiva learns from the Pasuk "u'Vas Kohen Ki Sihyeh l'Ish Zar" - that the Bi'ah of any man (even without betrothal) who is unfit to marry a bas Kohen makes her a Zonah and forbids her to eat Terumah and to marry a Kohen.

(b)Rebbi Akiva ultimately learns the Isur of a Sotah to her husband, the Bo'el, to a Kohen and the Isur to eat Terumah from four Pesukim - the three "Nitma'ah" and the one 'Vav' in "V'Nitma'ah".

2)

(a)Rebbi Yishmael does not Darshan the 'Vav' in "Venit'ama'h", so he only has the three Pesukim of "Nitma'ah" - from which he Darshens 'le'Ba'al', 'leBo'el' and 'li'Terumah'.

(b)In fact, he learns Kehunah from a 'Kal va'Chomer'. He prefers to learn Terumah from a Pasuk and Kehunah from a 'Kal va'Chomer', rather then Kehunah from a Pasuk in which case, the Sotah would be permitted to eat Terumah - because it is logical to establish the third Derashah by Terumah, which like Ba'al and Bo'el, applies in the lifetime of the husband, rather than by Kehunah, which only applies after his death.

(c)Rebbi Akiva on the other hand, requires four Pesukim. The reason that the Torah needs four Pesukim, and will not suffice with three plus the 'Kal va'Chomer' (like Rebbi Yishmael) may be because he disagrees with Rebbi Yishmael's Sevara (that the third Derashah must be similar to Ba'al and Bo'el). Alternatively, to answer the Kashya, we might rely on the principle - 'Milsa d'Asya b'Kal va'Chomer, Tarach v'Kasav Lah K'ra' (the Torah specifically included a Pasuk for Kehunah, despite the fact that we would have known it from a 'Kal va'Chomer' from Terumah anyway).

3)

(a)We can extrapolate from the Pasuk ...

1. ... "veha'Basar Asher Yiga b'Chol Tamei Lo Ye'achel" - that if it is only a Safek Tum'ah, then one may eat it (without becoming Tamei).

2. ... "veha'Basar Kol Tahor Yochal Basar" - that if it is a Safek Tamei, then one cannot eat it (without becoming Tamei).

(b)Rav Gidal Amar Rav learns from this apparent contradiction - that when the Safek is able to ask, he is Tamei in the Reshus ha'Yachid, whereas when it is not, it is Tahor.

(c)In view of ...

1. ... Rav Gidal's Derashah, we nevertheless need to learn the Din of Da'as Lisha'el from Sotah - to confine the Tum'ah in a case of 'Ein Lah Da'as Lishaeil' to a Reshus ha'Yachid, like by Sotah.

2. ... the source of Sotah, we nevertheless need Rav Gidal's Derashah - to teach us that Da'as Lisha'el is Tamei even if it is only the Safek that is able to ask, whereas from Sotah we would have derived that both the Safek and the Tamei 'object' must both be in that category in order to be Tamei.

4)

(a)The problem with Raban Yochanan ben Zakai in our Mishnah, who holds that everyone agrees with the concept of a Shlishi l'Tum'ah at least in Terumah; however, since he could not find a Pasuk for it, a generation would arise who would declare it Tahor. The problem with this is - if he had no Pasuk for a Shlishi l'Tum'ah, why should they not declare it Tahor?

(b)Rav Yehudah Amar Rav cites a 'Kal va'Chomer' from a Tvul Yom - who is permitted to eat Chulin, yet he invalidates Terumah, a Sheni, which is Pasul by Chulin, should certainly make a Terumah a Shlishi.

(c)We cannot apply the principle of 'Dayo' (to restrict the level of Tum'ah to a Sheni, because we start off with a loaf which is a Sheni, so we cannot learn anything beyond a Sheni from the 'Kal va'Chomer') because we know that a Sheni makes Terumah Pasul without a Kal va'Chomer, and our Gemara maintains that where the 'Kal va'Chomer' will not achieve anything new if 'Dayo' is applied, then we do not apply it.

5)

(a)We refute ...

1. ... the 'Kal va'Chomer' however - on the grounds that a Tvul-Yom (a Tamei person who has Toveled and who is waiting for nightfall) is an Av ha'Tum'ah, whereas a loaf that is a Sheni is only a Toldah.

2. ... the suggestion that we are speaking about a Tvul-Yom of a Sheretz, who is only a Sheni, and who nevertheless, invalidates Terumah - on the grounds that even a Tvul Yom of a Sheretz (i.e. a person) is of the species that can become an Av ha'Tum'ah (through contact with a corpse); whereas a loaf which is a Sheni is not.

(b)Food cannot become an Av ha'Tum'ah - because when the Torah speaks about a Tamei Mes becoming an Av, it has just spoken about Taharah b'Mikvah, and food cannot be purified in a Mikvah.

6)

(a)It is in order to bring a support for the 'Mah Matzinu' from a Tvul-Yom of a Sheretz, from earthenware vessels (which cannot become an Av ha'Tum'ah), in spite of the fact that they are different, inasmuch as they are not permitted by Chulin (like a Tvul-Yom of a Sheretz is) - because since we are basically learning a Chumra, it does not matter that they do not possess the Kula which sparks off the 'Mah Matzinu'. All that matters is that they don't possess the Chumra which creates the Pircha.

(b)We refute the suggestion to learn a loaf which is a Sheni from an earthenware vessel (which cannot become an Av ha'Tum'ah, and yet it can invalidate Terumah on the grounds that earthenware vessels are different) - inasmuch as they can receive Tum'ah from the inside (even when there is no physical contact between them).

(c)Raban Yachanan ben Zakai ultimately learns that a loaf of bread that is a Sheni can make a Shlishi in Terumah - from a 'Mah ha'Tzad' (a combination of a Tvul-Yom and earthenware vessels (which are both permitted by Chulin but render Pasul by Terumah).

7)

(a)We change the current text of the 'Mah ha'Tzad' (from she'Mutarin b'Chulin u'Poslin bi'Terumah') to 'she'Temei'in u'Poslin bi'Terumah'. We initially attempt to explain 'u'Poslin bi'Terumah' with regard to Klei Cheres - by establishing the case by earthenware vessels that are covered and sealed tightly shut, in which case the vessel protects Chulin that it contains from Ohel ha'Mes, but not Terumah.

(b)One of the reasons for refuting this explanation is because the implications from a Sugya in Chagigah are that it protects Terumah, too. The second reason is - because the phrase 'u'Poslin bi'Terumah' would then be inappropriate (since the correct wording would have been 've'Eino Matzeles bi'Terumah).

(c)Our main objection to the current text 'she'Mutarin b'Chulin' is - because 'she'Mutarin l'Chulin' is a Kula and not a Chumra.

8)

(a)We learn from the Pasuk "U'va ha'Shemesh Ve'taher" - that a Tvul Yom is considered Tamei.

(b)The later generation, that declares a Shlishi l'Tum'ah Tahor, according to Raban Yochanan ben Zakai, will reject the 'Tzad ha'Shaveh' because of the Pircha of 'Tzad Chamur' (which he does not consider a Pircha) - meaning that each of the Pirchos is particularly radical, and can therefore not combine to include a Sheni l'Tum'ah, which does not possess such a radical Chumra.

9)

(a)Rebbi Yosi learns from the Pasuk "v'ha'Basar Asher Yiga b'Chol Tamei, Lo Ye'achel" - that there is a Shlishi in Chulin (seeing as the Pasuk incorporates meat that touches a Sheni).

(b)He goes on to learn from a 'Kal va'Chomer' from Mechusar Kipurim, that a Revi'i ba'Kodesh is Pasul - because, if a Mechusar Kipurim, who is permitted to eat Terumah, renders Kodesh Pasul, then a Shlishi, who is Pasul to eat Terumah, should certainly render Kodesh, Pasul.

(c)We might have applied here the principle of 'Dayo Lavo Min ha'Din Liheyos ka'Nadun' - and restrict the Derashah to making a Shlishi, like a Mechusar Kipurim, from which we are learning it.

(d)We do not however, apply it - because, as we explained earlier, whenever 'Dayo' renders the 'Kal va'Chomer ineffective, we ignore it (and here too, we already know that a Shlishi is Pasul.

10)

(a)Rebbi Yochanan queries Rebbi Yosi from the opinion of the Rabanan in a Beraisa, who say that food of Kodesh or Terumah that touched a Tvul-Yom is Pasul, yet it does not make a Revi'i ba'Kodesh. Rebbi Meir considers a Tvul-Yom a Sheni with regard to Kodesh (like with regard to Terumah). Practically, this means - that it is Metamei one and Pasels one.

(b)Aba Shaul says - that a Tvul-Yom has the Din of a Rishon as regards Tum'ah, which means that it is Metamei two, and Pasels one

11)

(a)Rav Papa suggests that Rebbi Yosi holds like Aba Shaul. He mentions Aba Shaul (and not Rebbi Meir) as if to say 'Who says that Rebbi Yosi is not even as strict as Aba Shaul'?

(b)We answer that if Rebbi Yosi held like Aba Shaul, he would learn a Revi'i ba'Kodesh from food that touched a Tvul-Yom (rather than from a Mechusar Kipurim) - because if food that comes from a Tvul-Yom (which is itself permitted to eat Chulin) makes a Revi'i, then a Shlishi that comes from a Sheni (who is forbidden to eat Chulin), should certainly make a Revi'i.

(c)We refute the Kashya that we cannot learn from a Tvul-Yom, since it is an Av ha'Tum'ah (like we asked above) - since it is clear that Rebbi Yosi does not consider this a Kashya.