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1)

(a) Having established that Ze'iri (who adds Se'or to the list of 'Heter Mitztaref le'Isur') holds like Rebbi Eliezer, he will also have to agree that there is a La'av by Ta'aroves Chametz on Pesach (like we learnt in our Mishnah). Note: Heter Mitztaref le'Isur is a branch of Ta'aroves of less than a k'Zayis Bichedei Achilas P'ras.

(b) The reason that Ze'iri mentions 'Se'or' - is to preclude from Abaye, who explains that "Kol" by Se'or comes to be Mechayev for burning half a k'Zayis on its own, as is implied by the Derashah (See last answer on previous Amud).

(a) If a Tevul-Yom touched the spices in a Chulin-stew containing Terumah spices - he only renders the location where he touched, Tamei.

(b) Abaye explains Rabah bar bar Chanah's statement (that a Zar receives Malkos for eating a k'Zayis) - to mean that he ate an overall k'Zayis (incorporating Heter and Isur), a proof that 'Heter Mitztaref le'Isur' applies even to other Isurim too (and is not confined to Nazir).

(c) Rav Dimi answers - that he is Chayav, not because of 'Heter Mitztaref le'Isur', but because there was a 'k'Zayis Bichedei Achilas P'ras' (for which everyone agrees, he is Chayav).

(d) A 'k'Zayis bi'Chedei Achilas Peras' - means that there is at least a k'Zayis for every four k'Beitzim (in which case whenever he eats four k'Beitzim, he has eaten a k'Zayis. In fact, this is also the maxumum time period within which one must eat a k'Zayis (i.e. the time it takes to eat four eggs) in order to be Chayav for eating a k'Zayis of any Isur, even when it is not mixed.

(a) The source for the Shiur of 'k'Zayis bi'Chedei Achilas Peras' - is Halachah le'Moshe mi'Sinai.

(b) The Rabbanan argue with Rebbi Eliezer and exempt one from Malkos for eating Kutach ha'Bavli - because Kutach ha'Bavli is a sharp condiment, and one does not tend to eat a k'Zayis bi'Chedei Achilas Peras'.

(c) Even if someone *does* eat a dish-full of Kutach ha'Bavli in one sitting he will not be Chayav - because this is not the normal way of eating it, and we will apply the principle of 'Batlah Da'ato Eitzel B'nei Adam'.

(a) If two mortars full of spice, one of Chulin, the other of Terumah, spill into two pots, one of Chulin and the other, of Terumah, we assume that the Terumah fell into the Terumah, and the Chulin into the Chulin - because by Isurim d'Rabbanan we apply the principle of 'Tolin' (meaning that we presume to the lenient side).

(b) The Beraisa is lenient by Terumah, to rely on Tolin - by the Terumah of spices, which is only mi'd'Rabbanan.

(c) Similarly, the second Beraisa relies on 'Tolin' in the case of two Sa'ah one of Chulin and one of Terumah, which fell into two boxes, one of Chulin and one of Terumah - because it is speaking about Terumah bi'Zeman ha'Zeh, which is d'Rabbanan.

5)

(a) 'Heter Mitztaref le'Isur' - is when half a Shiur of Heter combines with half a Shiur of Isur; whereas 'Ta'am k'Ikar' - is when the taste of the Isur becomes absorbed in the Heter.

(b) The Beraisa, which learns 'Ta'am k'Ikar' from "Mishras", follows the opinion of the Rabbanan (of Rebbi Akiva, who do *not* learn 'Heter Mitztaref le'Isur' from "Mishras"), whereas Rebbi Yochanan and Zeiri, follow that of Rebbi Akiva (who *does*).

(c) A Nazir is not permanently forbidden to drink wine (only for as long as he undertook to be a Nazir), it does not incorporate an Isur Hana'ah and it can become permitted (by releasing the nazarite vow through a Chacham); 'Kil'ayim' is a permanent Isur (once one sows the forbidden seeds, they are forbidden permanently), it is Asur be'Hana'ah and there is no way that the Isur can become permitted).

(d) Orlah is not a permanent Isur, since, after three years, the seeds become permitted.

(a) When Rebbi Akiva says in Nazir 'Nazir she'Sharah Pito ba'Yayin, ve'Yesh Bo Letzaref Kedei k'Zayis, Chayav', who says that this is because of Heter Mitztaref le'Isur? Perhaps it speaks when there is a full k'Zayis of wine, and he is Chayav because of Ta'aroves.

(b) Even though Rebbi Akiva is referring to the wine alone, he nevertheless gives the Shiur as a k'Zayis, and not a Revi'is, because that is the Shiur of a Nazir, even by a liquid - 'Halachah le'Moshe mi'Sinai'.

(c) One measures a k'Zayis by liquid - by filling a receptacle to the brim, and slipping an olive into it. The amount of liquid that is displaced is a k'Zayis.

(d) Rebbi Akiva says in the Beraisa that if a Nazir soaked his bread in wine, and then proceeded to eat a k'Zayis of the bread, he is Chayav.

(a) In the previous case, if the Nazir ate *half* a k'Zayis of bread with wine absorbed in it, together with half a k'Zayis of dry bread, he is Chayav. If the wine had spread across the entire k'Zayis of bread, it would be a case of 'Ta'am k'Ikar', and the Rabbanan, who hold 'Ta'am k'Ikar d'Oraysa', would not disagree with Rebbi Akiva.

(b) In the current case, the Rabbanan hold that the Nazir is Patur.

(c) Rebbi Akiva learns 'Ta'am k'Ikar' from Basar be'Chalav.

(d) The Rabbanan decline to do so - because Basar be'Chalav is a Chidush (and we cannot use a Chidush as an example for other cases).

(a) It is not the fact that the two individual ingredients are permitted, and only become Asur when they are cooked - that make Basar be'Chalav unique, since Kil'ayim shares the same qualifications.

(b) What is unique about Basar be'Chalav is the fact that one can soak meat and milk together all day, and one will not have transgressed any Isur (either by soaking them or by then eating them) - yet the moment one cooks them together, one transgresses both the Isur of cooking Basar be'Chalav and that of eating it.

(c) Rebbi Akiva does not argue with that. He does not learn Ta'am k'Ikar from Basar be'Chalav, as we originally thought.

(d) He learns it from the Isur of Gi'uley Nochrim (the prohibition of using 'Tereifah' pots that have not been Kashered).

(a) When the Torah prescribed Hag'alah by the vessels captured from Midyan, it was referring to vessels that had been used that day (since that was 'Nosen Ta'am li'Shevach' - the taste which the food absorbed in the walls of the vessels is a pleasant one); whereas the taste that exudes from the walls of the vessel after twenty-four hours is 'Nosen Ta'am li'Fegam' (unpleasant, and spoils the food into which it is exuded).

(b) The Rabbanan hold that even though the taste of less than a day is not repugnant, it is inevitably slightly unpleasant, so it remains a Chidush, and we cannot learn Ta'am k'Ikar from it.