1)

(a)Rebbi Akiva cannot use the Kal va'Chomer to extend 'Heter Mitztaref l'Isur' from Nazir to all Isurim in the Torah - because the Pasuk by Chatas also teaches us 'Heter Mitztaref l'Isur', and 'Shnei Kesuvim ha'Ba'im k'Echad, Ein Melamdin'.

(b)We learn from the Pasuk in Tzav "Kol Asher Yiga bi'Vesarah Yikdash" - that anything (that is fit to become Kadosh) which touches a Chatas and absorbs from it, adopts the Kedushah of the Chatas.

(c)If a piece of Shelamim touched fat of a Kasher Chatas (see Mosaf Rashi) - one of which was hot - it must be eaten within the curtains of the Azarah, by male Kohanim only and only on the day it is brought plus the following night.

2)

(a)The Rabanan require "Mishras" by Nazir for 'Ta'am k'Ikar' (which we extend to the entire Torah), and "Kol Asher Yiga" etc. by Chatas for 'Heter Mitztaref l'Isur' (from which we cannot learn Chulin, since Chulin mi'Kodshim Lo Yalfinan).

(b)Rebbi Akiva, on the other hand, does consider them 'Shnei Kesuvim ha'Ba'im k'Echad' - because, according to him, both Pesukim are speaking about 'Heter Mitztaref l'Isur', making them 'Shnei Kesuvim ha'Ba'im k'Echad' - v'Ein Melamdin.

(c)According to him, we need the Pasuk by Nazir, because 'Chulin mi'Kodshim Lo Yalfinan'; but we do not need the Pasuk by Chatas, since we could learn it from Nazir, making it a case of 'Shnei Kesuvim ha'Ba'im k'Echad'.

3)

(a)We learn from the Pasuk in Naso "mi'Kol Asher Ye'aseh mi'Gefen ha'Yayin" - that all Isurei Nazir combine to make up the Shi'ur k'Zayis.

(b)According to Rebbi Akiva who learns 'Heter Mitztaref l'Isur' - we would not know from a Kal va'Chomer that Isur Mitztaref l'Isur - because whereas the former is speaking specifically when they are eaten simultaneously, the latter is speaking even when they are eaten one after the other (provided they are eaten within the time limit of 'Kedei Achilas Pras).

4)

(a)The Rabanan of Rebbi Eliezer do not learn 'Ta'am k'Ikar' from Gi'ulei Nochrim (like Rebbi Akiva), because they hold that Gi'ulei Nochrim is a Chidush (like the Rabanan); nor do they learn it from "Mishras" (like the Rabanan), because they use "Mishras" for Heter Mitztaref l'Isur (like Rebbi Akiva).

5)

(a)According to the Tana of our Mishnah, one is obligated to destroy the dough from the cracks of a dish - wherever there is at least a k'Zayis in one place.

(b)Rav Yehudah Amar Shmuel restricts the obligation to - where the dough has not been placed there to strengthen the dish, but if it has, then one is not obligated to destroy it, even if there is more than a k'Zayis in one place.

(c)We can deduce from the second Lashon (where Rav Yehudah Amar Shmuel restricts the leniency in the Seifa, which permits retaining less than a k'Zayis, to when the dough was put there to strengthen the dish) - that wherever there is more than a k'Zayis, it must be destroyed even if it was placed there to strengthen the dish.

6)

(a)Rav Huna resolves the two contradictory Beraisos, one which holds like the first Lashon of Shmuel, the other, like the second - by erasing the more lenient Beraisa (the one which holds like the first Lashon).

(b)The Tana Kama says that a block of yeast that has gone bad must nevertheless be destroyed - because it can be ground and used as yeast in many doughs.

(c)Rebbi Shimon ben Elazar says that dough that is designated for another use (even if it is more than a k'Zayis) becomes Batel - and he will be the author of the Beraisa which holds like Rav Yehudah Amar Shmuel's first Lashon, which permits even more than a k'Zayis of dough that is being used to strengthen the dish.

(d)Rav Yosef's explanation answers the discrepancy by more than a k'Zayis that is put there to strengthen the dish, Abaye points out. He does not however, address the discrepancy by less than a k'Zayis in the case of a dough that was not placed there to strengthen the dish, which the first Beraisa permits, whereas we have no proof that Rebbi Shimon ben Elazar (who is only lenient by dough that was specifically designated for another purpose) will permit any dough that still stands to be eaten.

7)

(a)In fact, the Gemara concludes, there are three locations, and three Dinim: 1. the base of the dish, which is a real Makom Lishah (and even a k'Zayis need not be removed). 2. The walls of the dish, which the first Beraisa refers to as 'she'Lo b'Makom Lishah' (though it is partially used during the Lishah, and where less than a k'Zayis is therefore permitted). 3. The outside of the dish, which is not a Makom Lishah at all (and which the second Beraisa refers to as 'she'Lo b'Makom Lishah') and where even less than a k'Zayis of dough is forbidden. Note: The first Beraisa does not address the outside of the dish at all; nor does the second Beraisa address its walls.

(b)Rav Ashi adds the top edge to the area of she'Lo b'Makom Lishah. Nor is this so obvious as it would at first appear - because sometimes, in the course of the kneading, the dough moves to the top of the dish, and the baker finds that he is actually kneading on the top edge of the dish.

8)

(a)Rav Nachman quoting Rav, who rules like Rebbi Shimon ben Elazar, will not require the block of dough to be cemented, since Rebbi Shimon ben Elazar permits it as it is. In that case, this ruling clashes with Rav Yitzchak bar Ashi, who, also quoting Rav, rules 'Im Tach Paneha b'Tit, Batlah' - from which we can infer that, if not, it is not Batel.

(b)Clearly, the Gemara concludes, Rav Nachman and Rav Yitzchak bar Ashi are at loggerheads over what Rav said, since each one quotes him differently.

(c)Two half-k'Zeisim in a dish combine to make up a k'Zayis - if they are joined by a strip of dough thick enough that, if one were to pick it up, both half-k'Zeisim would come up with it.

(d)If the two half-k'Zeisim of Chametz are found on the floor of the house, they will have the Din of a k'Zayis, even if they are not connected - because sometimes, they are placed together in the process of sweeping.

9)

(a)The Gemara's third She'eilah - is what the Din will be by two half-k'Zeisim in two rooms, one within the other.

(b)The three She'eilos are dependent upon each other: Assuming that by two rooms on two stories that the two half-k'Zeisim do not combine, that is because it is unlikely that they will ever fall in the same place, perhaps a half-k'Zayis in a room and a half-k'Zayis in an adjoining porch (where they are more likely to land up together, seeing as one tends to go from one to the other) will combine. And even assuming that in that case, they are considered one k'Zayis, that is because, as we explained, the two areas are constantly used together, this may not be the case, by two half-k'Zeisim in two rooms, one within each other, which (although they are more frequently used than two rooms on two stories) are less frequently used than a room and the adjoining porch.

10)

(a)According to the Tana Kama, moldy bread loses its status of bread ...

1. ... regarding Tum'as Ochlin - when a dog will no longer eat it.

2. ... regarding the prohibition of burning Terumah Tehorah together Terumah Temei'ah - already when it becomes unfit for a human-being to eat.

(b)Rebbi Nasan maintains that - the moment it becomes unfit for a human being, it loses its status as food even regarding Tum'as Ochlin.

11)

(a)According to the Tana Kama, flour that is placed into a tanning-bowl at least three days before Pesach becomes so smelly that it is no longer necessary to destroy it. This time period will apply whether there are already skins in the bowl or not.

(b)Rebbi Nasan holds - that, if there were skins in the bowl, then even if the flour was placed in the bowl shortly before Pesach, the flour loses its identity.

(c)Rava rules like Rebbi Nasan, even if the flour was placed one day and even one hour before Pesach.